examples/Petri/SimplePetriNets2.ipynb

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     "text": [
      "┌ Info: Precompiling DiffEqJump [c894b116-72e5-5b58-be3c-e6d8d4ac2b12]\n",
      "└ @ Base loading.jl:1342\n",
      "\u001b[33m\u001b[1m┌ \u001b[22m\u001b[39m\u001b[33m\u001b[1mWarning: \u001b[22m\u001b[39mModule DiffEqBase with build ID 18039643207670 is missing from the cache.\n",
      "\u001b[33m\u001b[1m│ \u001b[22m\u001b[39mThis may mean DiffEqBase [2b5f629d-d688-5b77-993f-72d75c75574e] does not support precompilation but is imported by a module that does.\n",
      "\u001b[33m\u001b[1m└ \u001b[22m\u001b[39m\u001b[90m@ Base loading.jl:1030\u001b[39m\n",
      "┌ Info: Skipping precompilation since __precompile__(false). Importing DiffEqJump [c894b116-72e5-5b58-be3c-e6d8d4ac2b12].\n",
      "└ @ Base loading.jl:1047\n"
     ]
    }
   ],
   "source": [
    "using AlgebraicPetri\n",
    "\n",
    "using OrdinaryDiffEq\n",
    "using StochasticDiffEq\n",
    "using DiffEqJump\n",
    "using Plots\n",
    "using LabelledArrays\n",
    "using Catlab\n",
    "using Catlab.Graphics\n",
    "using Catlab.WiringDiagrams\n",
    "using Catlab.CategoricalAlgebra\n",
    "using Catlab.Programs.RelationalPrograms\n",
    "\n",
    "display_uwd(ex) = to_graphviz(ex, box_labels=:name, junction_labels=:variable, edge_attrs=Dict(:len=>\".75\"));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "b653f118",
   "metadata": {},
   "outputs": [
    {
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       "<div class=\"c-set\">\n",
       "<span class=\"c-set-summary\">LabelledPetriNet with elements T = 1:2, S = 1:3, I = 1:3, O = 1:3</span>\n",
       "<table>\n",
       "  <thead>\n",
       "    <tr class = \"header headerLastRow\">\n",
       "      <th class = \"rowNumber\">T</th>\n",
       "      <th style = \"text-align: right;\">tname</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td class = \"rowNumber\">1</td>\n",
       "      <td style = \"text-align: right;\">inf</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td class = \"rowNumber\">2</td>\n",
       "      <td style = \"text-align: right;\">rec</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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       "      <th style = \"text-align: right;\">sname</th>\n",
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       "      <td style = \"text-align: right;\">I</td>\n",
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       "      <td class = \"rowNumber\">3</td>\n",
       "      <td style = \"text-align: right;\">R</td>\n",
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       "  </tbody>\n",
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       "<table>\n",
       "  <thead>\n",
       "    <tr class = \"header headerLastRow\">\n",
       "      <th class = \"rowNumber\">I</th>\n",
       "      <th style = \"text-align: right;\">it</th>\n",
       "      <th style = \"text-align: right;\">is</th>\n",
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       "      <th class = \"rowNumber\">O</th>\n",
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       "      <th style = \"text-align: right;\">os</th>\n",
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       "LabelledPetriNet with elements T = 1:2, S = 1:3, I = 1:3, O = 1:3\n",
       "┌───┬───────┐\n",
       "│\u001b[1m T \u001b[0m│\u001b[1m tname \u001b[0m│\n",
       "├───┼───────┤\n",
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       "└───┴───────┘\n",
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       "└───┴────┴────┘\n",
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   "source": [
    "sirLabeled = LabelledPetriNet([:S, :I, :R], :inf=>((:S,:I)=>(:I,:I)), :rec=>(:I=>:R))"
   ]
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       "  307.065,203.979 309.22,213.959 311.376,224.673 313.531,236.163 315.687,248.465 317.843,261.615 319.998,275.641 322.154,290.571 324.31,306.425 326.465,323.221 \n",
       "  328.621,340.975 330.777,359.695 332.932,379.381 335.088,400.024 337.243,421.605 339.399,444.094 341.555,467.454 343.71,491.637 345.866,516.587 348.022,542.238 \n",
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       "  414.846,1224.01 417.002,1234.42 419.157,1244.18 421.313,1253.32 423.469,1261.86 425.624,1269.83 427.78,1277.26 429.935,1284.19 432.091,1290.64 434.247,1296.64 \n",
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       "  479.515,1360.71 481.671,1362.04 483.826,1363.28 485.982,1364.44 488.137,1365.52 490.293,1366.54 492.449,1367.5 494.604,1368.39 496.76,1369.23 498.916,1370.02 \n",
       "  501.071,1370.76 503.227,1371.46 505.382,1372.12 507.538,1372.73 509.694,1373.31 511.849,1373.86 514.005,1374.37 516.161,1374.86 518.316,1375.31 520.472,1375.74 \n",
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       "  565.74,1380.9 567.896,1381.03 570.051,1381.16 572.207,1381.28 574.363,1381.39 576.518,1381.5 578.674,1381.6 580.829,1381.7 582.985,1381.79 585.141,1381.88 \n",
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       "  630.409,1383.06 632.564,1383.1 634.72,1383.13 636.876,1383.16 639.031,1383.19 641.187,1383.22 643.343,1383.25 645.498,1383.28 647.654,1383.3 649.81,1383.33 \n",
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       "  759.747,1383.93 761.902,1383.94 764.058,1383.94 766.213,1383.95 768.369,1383.95 770.525,1383.96 772.68,1383.96 774.836,1383.97 776.992,1383.97 779.147,1383.97 \n",
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       "  1061.53,1384.15 1063.69,1384.15 1065.85,1384.15 1068,1384.15 1070.16,1384.15 1072.31,1384.15 1074.47,1384.15 1076.62,1384.15 1078.78,1384.15 1080.94,1384.15 \n",
       "  1083.09,1384.15 1085.25,1384.15 1087.4,1384.15 1089.56,1384.15 1091.71,1384.15 1093.87,1384.15 1096.02,1384.15 1098.18,1384.16 1100.34,1384.16 1102.49,1384.16 \n",
       "  1104.65,1384.16 1106.8,1384.16 1108.96,1384.16 1111.11,1384.16 1113.27,1384.16 1115.43,1384.16 1117.58,1384.16 1119.74,1384.16 1121.89,1384.16 1124.05,1384.16 \n",
       "  1126.2,1384.16 1128.36,1384.16 1130.51,1384.16 1132.67,1384.16 1134.83,1384.16 1136.98,1384.16 1139.14,1384.16 1141.29,1384.16 1143.45,1384.16 1145.6,1384.16 \n",
       "  1147.76,1384.16 1149.92,1384.16 1152.07,1384.16 1154.23,1384.16 1156.38,1384.16 1158.54,1384.16 1160.69,1384.16 1162.85,1384.16 1165,1384.16 1167.16,1384.16 \n",
       "  1169.32,1384.16 1171.47,1384.16 1173.63,1384.16 1175.78,1384.16 1177.94,1384.16 1180.09,1384.16 1182.25,1384.16 1184.41,1384.16 1186.56,1384.16 1188.72,1384.16 \n",
       "  1190.87,1384.16 1193.03,1384.16 1195.18,1384.16 1197.34,1384.17 1199.49,1384.17 1201.65,1384.17 1203.81,1384.17 1205.96,1384.17 1208.12,1384.17 1210.27,1384.17 \n",
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       "  1233.98,1384.17 1236.14,1384.17 1238.3,1384.17 1240.45,1384.17 1242.61,1384.17 1244.76,1384.17 1246.92,1384.17 1249.07,1384.17 1251.23,1384.17 1253.39,1384.17 \n",
       "  1255.54,1384.17 1257.7,1384.17 1259.85,1384.17 1262.01,1384.17 1264.16,1384.17 1266.32,1384.17 1268.47,1384.17 1270.63,1384.17 1272.79,1384.17 1274.94,1384.17 \n",
       "  1277.1,1384.17 1279.25,1384.17 1281.41,1384.17 1283.56,1384.17 1285.72,1384.17 1287.88,1384.17 1290.03,1384.17 1292.19,1384.17 1294.34,1384.17 1296.5,1384.17 \n",
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       "  1320.21,1384.17 1322.37,1384.17 1324.52,1384.17 1326.68,1384.17 1328.83,1384.17 1330.99,1384.17 1333.14,1384.17 1335.3,1384.17 1337.45,1384.17 1339.61,1384.17 \n",
       "  1341.77,1384.17 1343.92,1384.17 1346.08,1384.17 1348.23,1384.17 1350.39,1384.17 1352.54,1384.17 1354.7,1384.17 1356.86,1384.17 1359.01,1384.17 1361.17,1384.17 \n",
       "  1363.32,1384.17 1365.48,1384.17 1367.63,1384.17 1369.79,1384.17 1371.95,1384.17 1374.1,1384.17 1376.26,1384.17 1378.41,1384.17 1380.57,1384.17 1382.72,1384.17 \n",
       "  1384.88,1384.17 1387.03,1384.17 1389.19,1384.17 1391.35,1384.17 1393.5,1384.17 1395.66,1384.17 1397.81,1384.17 1399.97,1384.17 1402.12,1384.17 1404.28,1384.17 \n",
       "  1406.44,1384.17 1408.59,1384.17 1410.75,1384.17 1412.9,1384.17 1415.06,1384.17 1417.21,1384.17 1419.37,1384.17 1421.52,1384.17 1423.68,1384.17 1425.84,1384.17 \n",
       "  1427.99,1384.17 1430.15,1384.17 1432.3,1384.17 1434.46,1384.17 1436.61,1384.17 1438.77,1384.18 1440.93,1384.18 1443.08,1384.18 1445.24,1384.18 1447.39,1384.18 \n",
       "  1449.55,1384.18 1451.7,1384.18 1453.86,1384.18 1456.01,1384.18 1458.17,1384.18 1460.33,1384.18 1462.48,1384.18 1464.64,1384.18 1466.79,1384.18 1468.95,1384.18 \n",
       "  1471.1,1384.18 1473.26,1384.18 1475.42,1384.18 1477.57,1384.18 1479.73,1384.18 1481.88,1384.18 1484.04,1384.18 1486.19,1384.18 1488.35,1384.18 1490.5,1384.18 \n",
       "  1492.66,1384.18 1494.82,1384.18 1496.97,1384.18 1499.13,1384.18 1501.28,1384.18 1503.44,1384.18 1505.59,1384.18 1507.75,1384.18 1509.91,1384.18 1512.06,1384.18 \n",
       "  1514.22,1384.18 1516.37,1384.18 1518.53,1384.18 1520.68,1384.18 1522.84,1384.18 1524.99,1384.18 1527.15,1384.18 1529.31,1384.18 1531.46,1384.18 1533.62,1384.18 \n",
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       "  1557.33,1384.18 1559.48,1384.18 1561.64,1384.18 1563.8,1384.18 1565.95,1384.18 1568.11,1384.18 1570.26,1384.18 1572.42,1384.18 1574.57,1384.18 1576.73,1384.18 \n",
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       "  1600.44,1384.18 1602.6,1384.18 1604.75,1384.18 1606.91,1384.18 1609.06,1384.18 1611.22,1384.18 1613.38,1384.18 1615.53,1384.18 1617.69,1384.18 1619.84,1384.18 \n",
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       "  1643.55,1384.18 1645.71,1384.18 1647.87,1384.18 1650.02,1384.18 1652.18,1384.18 1654.33,1384.18 1656.49,1384.18 1658.64,1384.18 1660.8,1384.18 1662.95,1384.18 \n",
       "  1665.11,1384.18 1667.27,1384.18 1669.42,1384.18 1671.58,1384.18 1673.73,1384.18 1675.89,1384.18 1678.04,1384.18 1680.2,1384.18 1682.36,1384.18 1684.51,1384.18 \n",
       "  1686.67,1384.18 1688.82,1384.18 1690.98,1384.18 1693.13,1384.18 1695.29,1384.18 1697.44,1384.18 1699.6,1384.18 1701.76,1384.18 1703.91,1384.18 1706.07,1384.18 \n",
       "  1708.22,1384.18 1710.38,1384.18 1712.53,1384.18 1714.69,1384.18 1716.85,1384.18 1719,1384.18 1721.16,1384.18 1723.31,1384.18 1725.47,1384.18 1727.62,1384.18 \n",
       "  1729.78,1384.18 1731.93,1384.18 1734.09,1384.18 1736.25,1384.18 1738.4,1384.18 1740.56,1384.18 1742.71,1384.18 1744.87,1384.18 1747.02,1384.18 1749.18,1384.18 \n",
       "  1751.34,1384.18 1753.49,1384.18 1755.65,1384.18 1757.8,1384.18 1759.96,1384.18 1762.11,1384.18 1764.27,1384.18 1766.42,1384.18 1768.58,1384.18 1770.74,1384.18 \n",
       "  1772.89,1384.18 1775.05,1384.18 1777.2,1384.18 1779.36,1384.18 1781.51,1384.18 1783.67,1384.18 1785.83,1384.18 1787.98,1384.18 1790.14,1384.18 1792.29,1384.18 \n",
       "  1794.45,1384.18 1796.6,1384.18 1798.76,1384.18 1800.92,1384.18 1803.07,1384.18 1805.23,1384.18 1807.38,1384.18 1809.54,1384.18 1811.69,1384.18 1813.85,1384.18 \n",
       "  1816,1384.18 1818.16,1384.18 1820.32,1384.18 1822.47,1384.18 1824.63,1384.18 1826.78,1384.18 1828.94,1384.18 1831.09,1384.18 1833.25,1384.18 1835.41,1384.18 \n",
       "  1837.56,1384.18 1839.72,1384.18 1841.87,1384.18 1844.03,1384.18 1846.18,1384.18 1848.34,1384.18 1850.49,1384.18 1852.65,1384.18 1854.81,1384.18 1856.96,1384.18 \n",
       "  1859.12,1384.18 1861.27,1384.18 1863.43,1384.18 1865.58,1384.18 1867.74,1384.18 1869.9,1384.18 1872.05,1384.18 1874.21,1384.18 1876.36,1384.18 1878.52,1384.18 \n",
       "  1880.67,1384.18 1882.83,1384.18 1884.98,1384.18 1887.14,1384.18 1889.3,1384.18 1891.45,1384.18 1893.61,1384.18 1895.76,1384.18 1897.92,1384.18 1900.07,1384.18 \n",
       "  1902.23,1384.18 1904.39,1384.18 1906.54,1384.18 1908.7,1384.18 1910.85,1384.18 1913.01,1384.18 1915.16,1384.18 1917.32,1384.18 1919.47,1384.18 1921.63,1384.18 \n",
       "  1923.79,1384.18 1925.94,1384.18 1928.1,1384.18 1930.25,1384.18 1932.41,1384.18 1934.56,1384.18 1936.72,1384.18 1938.88,1384.18 1941.03,1384.18 1943.19,1384.18 \n",
       "  1945.34,1384.18 1947.5,1384.18 1949.65,1384.18 1951.81,1384.18 1953.96,1384.18 1956.12,1384.18 1958.28,1384.18 1960.43,1384.18 1962.59,1384.18 1964.74,1384.18 \n",
       "  1966.9,1384.18 1969.05,1384.18 1971.21,1384.18 1973.37,1384.18 1975.52,1384.18 1977.68,1384.18 1979.83,1384.18 1981.99,1384.18 1984.14,1384.18 1986.3,1384.18 \n",
       "  1988.45,1384.18 1990.61,1384.18 1992.77,1384.18 1994.92,1384.18 1997.08,1384.18 1999.23,1384.18 2001.39,1384.18 2003.54,1384.18 2005.7,1384.18 2007.86,1384.18 \n",
       "  2010.01,1384.18 2012.17,1384.18 2014.32,1384.18 2016.48,1384.18 2018.63,1384.18 2020.79,1384.18 2022.94,1384.18 2025.1,1384.18 2027.26,1384.18 2029.41,1384.18 \n",
       "  2031.57,1384.18 2033.72,1384.18 2035.88,1384.18 2038.03,1384.18 2040.19,1384.18 2042.35,1384.18 2044.5,1384.18 2046.66,1384.18 2048.81,1384.18 2050.97,1384.18 \n",
       "  2053.12,1384.18 2055.28,1384.18 2057.43,1384.18 2059.59,1384.18 2061.75,1384.18 2063.9,1384.18 2066.06,1384.18 2068.21,1384.18 2070.37,1384.18 2072.52,1384.18 \n",
       "  2074.68,1384.18 2076.84,1384.18 2078.99,1384.18 2081.15,1384.18 2083.3,1384.18 2085.46,1384.18 2087.61,1384.18 2089.77,1384.18 2091.92,1384.18 2094.08,1384.18 \n",
       "  2096.24,1384.18 2098.39,1384.18 2100.55,1384.18 2102.7,1384.18 2104.86,1384.18 2107.01,1384.18 2109.17,1384.18 2111.33,1384.18 2113.48,1384.18 2115.64,1384.18 \n",
       "  2117.79,1384.18 2119.95,1384.18 2122.1,1384.18 2124.26,1384.18 2126.41,1384.18 2128.57,1384.18 2130.73,1384.18 2132.88,1384.18 2135.04,1384.18 2137.19,1384.18 \n",
       "  2139.35,1384.18 2141.5,1384.18 2143.66,1384.18 2145.82,1384.18 2147.97,1384.18 2150.13,1384.18 2152.28,1384.18 2154.44,1384.18 2156.59,1384.18 2158.75,1384.18 \n",
       "  2160.9,1384.18 2163.06,1384.18 2165.22,1384.18 2167.37,1384.18 2169.53,1384.18 2171.68,1384.18 2173.84,1384.18 2175.99,1384.18 2178.15,1384.18 2180.31,1384.18 \n",
       "  2182.46,1384.18 2184.62,1384.18 2186.77,1384.18 2188.93,1384.18 2191.08,1384.18 2193.24,1384.18 2195.4,1384.18 2197.55,1384.18 2199.71,1384.18 2201.86,1384.18 \n",
       "  2204.02,1384.18 2206.17,1384.18 2208.33,1384.18 2210.48,1384.18 2212.64,1384.18 2214.8,1384.18 2216.95,1384.18 2219.11,1384.18 2221.26,1384.18 2223.42,1384.18 \n",
       "  2225.57,1384.18 2227.73,1384.18 2229.89,1384.18 2232.04,1384.18 2234.2,1384.18 2236.35,1384.18 2238.51,1384.18 2240.66,1384.18 2242.82,1384.18 2244.97,1384.18 \n",
       "  2247.13,1384.18 2249.29,1384.18 2251.44,1384.18 2253.6,1384.18 2255.75,1384.18 2257.91,1384.18 2260.06,1384.18 2262.22,1384.18 2264.38,1384.18 2266.53,1384.18 \n",
       "  2268.69,1384.18 2270.84,1384.18 2273,1384.18 2275.15,1384.18 2277.31,1384.18 2279.46,1384.18 2281.62,1384.18 2283.78,1384.18 2285.93,1384.18 2288.09,1384.18 \n",
       "  2290.24,1384.18 2292.4,1384.18 2294.55,1384.18 2296.71,1384.18 2298.87,1384.18 2301.02,1384.18 2303.18,1384.18 2305.33,1384.18 2307.49,1384.18 2309.64,1384.18 \n",
       "  2311.8,1384.18 2313.95,1384.18 2316.11,1384.18 2318.27,1384.18 2320.42,1384.18 2322.58,1384.18 2324.73,1384.18 2326.89,1384.18 2329.04,1384.18 2331.2,1384.18 \n",
       "  2333.36,1384.18 2335.51,1384.18 2337.67,1384.18 2339.82,1384.18 2341.98,1384.18 2344.13,1384.18 2346.29,1384.18 2348.44,1384.18 2350.6,1384.18 2352.76,1384.18 \n",
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       "  220.839,1381.05 222.995,1380.75 225.151,1380.42 227.306,1380.06 229.462,1379.67 231.618,1379.24 233.773,1378.77 235.929,1378.26 238.085,1377.7 240.24,1377.09 \n",
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       "  285.508,1338.55 287.664,1334.45 289.82,1330 291.975,1325.17 294.131,1319.94 296.286,1314.29 298.442,1308.17 300.598,1301.56 302.753,1294.43 304.909,1286.76 \n",
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       "  1277.1,1364.91 1279.25,1365.1 1281.41,1365.29 1283.56,1365.48 1285.72,1365.66 1287.88,1365.85 1290.03,1366.03 1292.19,1366.21 1294.34,1366.39 1296.5,1366.57 \n",
       "  1298.65,1366.75 1300.81,1366.92 1302.96,1367.09 1305.12,1367.26 1307.28,1367.43 1309.43,1367.6 1311.59,1367.77 1313.74,1367.93 1315.9,1368.09 1318.05,1368.25 \n",
       "  1320.21,1368.41 1322.37,1368.57 1324.52,1368.73 1326.68,1368.88 1328.83,1369.03 1330.99,1369.18 1333.14,1369.33 1335.3,1369.48 1337.45,1369.63 1339.61,1369.77 \n",
       "  1341.77,1369.92 1343.92,1370.06 1346.08,1370.2 1348.23,1370.34 1350.39,1370.48 1352.54,1370.62 1354.7,1370.75 1356.86,1370.89 1359.01,1371.02 1361.17,1371.15 \n",
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       "  1427.99,1374.64 1430.15,1374.74 1432.3,1374.83 1434.46,1374.93 1436.61,1375.02 1438.77,1375.11 1440.93,1375.2 1443.08,1375.29 1445.24,1375.38 1447.39,1375.47 \n",
       "  1449.55,1375.56 1451.7,1375.64 1453.86,1375.73 1456.01,1375.81 1458.17,1375.9 1460.33,1375.98 1462.48,1376.06 1464.64,1376.14 1466.79,1376.22 1468.95,1376.3 \n",
       "  1471.1,1376.38 1473.26,1376.46 1475.42,1376.54 1477.57,1376.61 1479.73,1376.69 1481.88,1376.76 1484.04,1376.84 1486.19,1376.91 1488.35,1376.99 1490.5,1377.06 \n",
       "  1492.66,1377.13 1494.82,1377.2 1496.97,1377.27 1499.13,1377.34 1501.28,1377.41 1503.44,1377.48 1505.59,1377.54 1507.75,1377.61 1509.91,1377.68 1512.06,1377.74 \n",
       "  1514.22,1377.81 1516.37,1377.87 1518.53,1377.93 1520.68,1378 1522.84,1378.06 1524.99,1378.12 1527.15,1378.18 1529.31,1378.24 1531.46,1378.3 1533.62,1378.36 \n",
       "  1535.77,1378.42 1537.93,1378.48 1540.08,1378.53 1542.24,1378.59 1544.4,1378.65 1546.55,1378.7 1548.71,1378.76 1550.86,1378.81 1553.02,1378.87 1555.17,1378.92 \n",
       "  1557.33,1378.97 1559.48,1379.03 1561.64,1379.08 1563.8,1379.13 1565.95,1379.18 1568.11,1379.23 1570.26,1379.28 1572.42,1379.33 1574.57,1379.38 1576.73,1379.43 \n",
       "  1578.89,1379.47 1581.04,1379.52 1583.2,1379.57 1585.35,1379.62 1587.51,1379.66 1589.66,1379.71 1591.82,1379.75 1593.97,1379.8 1596.13,1379.84 1598.29,1379.88 \n",
       "  1600.44,1379.93 1602.6,1379.97 1604.75,1380.01 1606.91,1380.06 1609.06,1380.1 1611.22,1380.14 1613.38,1380.18 1615.53,1380.22 1617.69,1380.26 1619.84,1380.3 \n",
       "  1622,1380.34 1624.15,1380.38 1626.31,1380.42 1628.46,1380.45 1630.62,1380.49 1632.78,1380.53 1634.93,1380.57 1637.09,1380.6 1639.24,1380.64 1641.4,1380.67 \n",
       "  1643.55,1380.71 1645.71,1380.74 1647.87,1380.78 1650.02,1380.81 1652.18,1380.85 1654.33,1380.88 1656.49,1380.92 1658.64,1380.95 1660.8,1380.98 1662.95,1381.01 \n",
       "  1665.11,1381.05 1667.27,1381.08 1669.42,1381.11 1671.58,1381.14 1673.73,1381.17 1675.89,1381.2 1678.04,1381.23 1680.2,1381.26 1682.36,1381.29 1684.51,1381.32 \n",
       "  1686.67,1381.35 1688.82,1381.38 1690.98,1381.41 1693.13,1381.44 1695.29,1381.46 1697.44,1381.49 1699.6,1381.52 1701.76,1381.55 1703.91,1381.57 1706.07,1381.6 \n",
       "  1708.22,1381.62 1710.38,1381.65 1712.53,1381.68 1714.69,1381.7 1716.85,1381.73 1719,1381.75 1721.16,1381.78 1723.31,1381.8 1725.47,1381.83 1727.62,1381.85 \n",
       "  1729.78,1381.87 1731.93,1381.9 1734.09,1381.92 1736.25,1381.94 1738.4,1381.97 1740.56,1381.99 1742.71,1382.01 1744.87,1382.03 1747.02,1382.06 1749.18,1382.08 \n",
       "  1751.34,1382.1 1753.49,1382.12 1755.65,1382.14 1757.8,1382.16 1759.96,1382.18 1762.11,1382.2 1764.27,1382.22 1766.42,1382.24 1768.58,1382.26 1770.74,1382.28 \n",
       "  1772.89,1382.3 1775.05,1382.32 1777.2,1382.34 1779.36,1382.36 1781.51,1382.38 1783.67,1382.4 1785.83,1382.41 1787.98,1382.43 1790.14,1382.45 1792.29,1382.47 \n",
       "  1794.45,1382.49 1796.6,1382.5 1798.76,1382.52 1800.92,1382.54 1803.07,1382.56 1805.23,1382.57 1807.38,1382.59 1809.54,1382.6 1811.69,1382.62 1813.85,1382.64 \n",
       "  1816,1382.65 1818.16,1382.67 1820.32,1382.68 1822.47,1382.7 1824.63,1382.72 1826.78,1382.73 1828.94,1382.75 1831.09,1382.76 1833.25,1382.78 1835.41,1382.79 \n",
       "  1837.56,1382.8 1839.72,1382.82 1841.87,1382.83 1844.03,1382.85 1846.18,1382.86 1848.34,1382.87 1850.49,1382.89 1852.65,1382.9 1854.81,1382.91 1856.96,1382.93 \n",
       "  1859.12,1382.94 1861.27,1382.95 1863.43,1382.97 1865.58,1382.98 1867.74,1382.99 1869.9,1383 1872.05,1383.02 1874.21,1383.03 1876.36,1383.04 1878.52,1383.05 \n",
       "  1880.67,1383.06 1882.83,1383.08 1884.98,1383.09 1887.14,1383.1 1889.3,1383.11 1891.45,1383.12 1893.61,1383.13 1895.76,1383.14 1897.92,1383.15 1900.07,1383.17 \n",
       "  1902.23,1383.18 1904.39,1383.19 1906.54,1383.2 1908.7,1383.21 1910.85,1383.22 1913.01,1383.23 1915.16,1383.24 1917.32,1383.25 1919.47,1383.26 1921.63,1383.27 \n",
       "  1923.79,1383.28 1925.94,1383.29 1928.1,1383.3 1930.25,1383.31 1932.41,1383.31 1934.56,1383.32 1936.72,1383.33 1938.88,1383.34 1941.03,1383.35 1943.19,1383.36 \n",
       "  1945.34,1383.37 1947.5,1383.38 1949.65,1383.39 1951.81,1383.39 1953.96,1383.4 1956.12,1383.41 1958.28,1383.42 1960.43,1383.43 1962.59,1383.44 1964.74,1383.44 \n",
       "  1966.9,1383.45 1969.05,1383.46 1971.21,1383.47 1973.37,1383.47 1975.52,1383.48 1977.68,1383.49 1979.83,1383.5 1981.99,1383.5 1984.14,1383.51 1986.3,1383.52 \n",
       "  1988.45,1383.53 1990.61,1383.53 1992.77,1383.54 1994.92,1383.55 1997.08,1383.55 1999.23,1383.56 2001.39,1383.57 2003.54,1383.57 2005.7,1383.58 2007.86,1383.59 \n",
       "  2010.01,1383.59 2012.17,1383.6 2014.32,1383.61 2016.48,1383.61 2018.63,1383.62 2020.79,1383.63 2022.94,1383.63 2025.1,1383.64 2027.26,1383.64 2029.41,1383.65 \n",
       "  2031.57,1383.66 2033.72,1383.66 2035.88,1383.67 2038.03,1383.67 2040.19,1383.68 2042.35,1383.68 2044.5,1383.69 2046.66,1383.69 2048.81,1383.7 2050.97,1383.71 \n",
       "  2053.12,1383.71 2055.28,1383.72 2057.43,1383.72 2059.59,1383.73 2061.75,1383.73 2063.9,1383.74 2066.06,1383.74 2068.21,1383.75 2070.37,1383.75 2072.52,1383.76 \n",
       "  2074.68,1383.76 2076.84,1383.77 2078.99,1383.77 2081.15,1383.78 2083.3,1383.78 2085.46,1383.78 2087.61,1383.79 2089.77,1383.79 2091.92,1383.8 2094.08,1383.8 \n",
       "  2096.24,1383.81 2098.39,1383.81 2100.55,1383.82 2102.7,1383.82 2104.86,1383.82 2107.01,1383.83 2109.17,1383.83 2111.33,1383.84 2113.48,1383.84 2115.64,1383.84 \n",
       "  2117.79,1383.85 2119.95,1383.85 2122.1,1383.86 2124.26,1383.86 2126.41,1383.86 2128.57,1383.87 2130.73,1383.87 2132.88,1383.87 2135.04,1383.88 2137.19,1383.88 \n",
       "  2139.35,1383.88 2141.5,1383.89 2143.66,1383.89 2145.82,1383.9 2147.97,1383.9 2150.13,1383.9 2152.28,1383.91 2154.44,1383.91 2156.59,1383.91 2158.75,1383.92 \n",
       "  2160.9,1383.92 2163.06,1383.92 2165.22,1383.92 2167.37,1383.93 2169.53,1383.93 2171.68,1383.93 2173.84,1383.94 2175.99,1383.94 2178.15,1383.94 2180.31,1383.95 \n",
       "  2182.46,1383.95 2184.62,1383.95 2186.77,1383.95 2188.93,1383.96 2191.08,1383.96 2193.24,1383.96 2195.4,1383.97 2197.55,1383.97 2199.71,1383.97 2201.86,1383.97 \n",
       "  2204.02,1383.98 2206.17,1383.98 2208.33,1383.98 2210.48,1383.98 2212.64,1383.99 2214.8,1383.99 2216.95,1383.99 2219.11,1383.99 2221.26,1384 2223.42,1384 \n",
       "  2225.57,1384 2227.73,1384 2229.89,1384.01 2232.04,1384.01 2234.2,1384.01 2236.35,1384.01 2238.51,1384.02 2240.66,1384.02 2242.82,1384.02 2244.97,1384.02 \n",
       "  2247.13,1384.02 2249.29,1384.03 2251.44,1384.03 2253.6,1384.03 2255.75,1384.03 2257.91,1384.03 2260.06,1384.04 2262.22,1384.04 2264.38,1384.04 2266.53,1384.04 \n",
       "  2268.69,1384.04 2270.84,1384.05 2273,1384.05 2275.15,1384.05 2277.31,1384.05 2279.46,1384.05 2281.62,1384.06 2283.78,1384.06 2285.93,1384.06 2288.09,1384.06 \n",
       "  2290.24,1384.06 2292.4,1384.06 2294.55,1384.07 2296.71,1384.07 2298.87,1384.07 2301.02,1384.07 2303.18,1384.07 2305.33,1384.07 2307.49,1384.08 2309.64,1384.08 \n",
       "  2311.8,1384.08 2313.95,1384.08 2316.11,1384.08 2318.27,1384.08 2320.42,1384.09 2322.58,1384.09 2324.73,1384.09 2326.89,1384.09 2329.04,1384.09 2331.2,1384.09 \n",
       "  2333.36,1384.09 2335.51,1384.1 2337.67,1384.1 2339.82,1384.1 2341.98,1384.1 2344.13,1384.1 2346.29,1384.1 2348.44,1384.1 2350.6,1384.11 2352.76,1384.11 \n",
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       "  953.753,172.796 955.909,171.933 958.064,171.078 960.22,170.231 962.376,169.394 964.531,168.564 966.687,167.743 968.843,166.93 970.998,166.125 973.154,165.328 \n",
       "  975.309,164.539 977.465,163.757 979.621,162.984 981.776,162.218 983.932,161.46 986.088,160.709 988.243,159.966 990.399,159.23 992.554,158.502 994.71,157.781 \n",
       "  996.866,157.067 999.021,156.36 1001.18,155.66 1003.33,154.967 1005.49,154.281 1007.64,153.602 1009.8,152.93 1011.96,152.264 1014.11,151.605 1016.27,150.952 \n",
       "  1018.42,150.306 1020.58,149.667 1022.73,149.034 1024.89,148.407 1027.04,147.786 1029.2,147.172 1031.36,146.563 1033.51,145.961 1035.67,145.365 1037.82,144.774 \n",
       "  1039.98,144.19 1042.13,143.611 1044.29,143.038 1046.45,142.471 1048.6,141.909 1050.76,141.353 1052.91,140.803 1055.07,140.258 1057.22,139.718 1059.38,139.184 \n",
       "  1061.53,138.655 1063.69,138.132 1065.85,137.613 1068,137.1 1070.16,136.592 1072.31,136.089 1074.47,135.591 1076.62,135.097 1078.78,134.609 1080.94,134.126 \n",
       "  1083.09,133.647 1085.25,133.173 1087.4,132.704 1089.56,132.24 1091.71,131.78 1093.87,131.324 1096.02,130.874 1098.18,130.427 1100.34,129.986 1102.49,129.548 \n",
       "  1104.65,129.115 1106.8,128.686 1108.96,128.262 1111.11,127.842 1113.27,127.426 1115.43,127.014 1117.58,126.606 1119.74,126.202 1121.89,125.803 1124.05,125.407 \n",
       "  1126.2,125.015 1128.36,124.627 1130.51,124.243 1132.67,123.863 1134.83,123.487 1136.98,123.114 1139.14,122.745 1141.29,122.38 1143.45,122.019 1145.6,121.661 \n",
       "  1147.76,121.306 1149.92,120.955 1152.07,120.608 1154.23,120.264 1156.38,119.924 1158.54,119.587 1160.69,119.253 1162.85,118.922 1165,118.595 1167.16,118.271 \n",
       "  1169.32,117.951 1171.47,117.633 1173.63,117.319 1175.78,117.008 1177.94,116.7 1180.09,116.395 1182.25,116.093 1184.41,115.794 1186.56,115.498 1188.72,115.205 \n",
       "  1190.87,114.915 1193.03,114.627 1195.18,114.343 1197.34,114.061 1199.49,113.783 1201.65,113.507 1203.81,113.233 1205.96,112.963 1208.12,112.695 1210.27,112.429 \n",
       "  1212.43,112.167 1214.58,111.907 1216.74,111.649 1218.9,111.395 1221.05,111.142 1223.21,110.892 1225.36,110.645 1227.52,110.4 1229.67,110.158 1231.83,109.918 \n",
       "  1233.98,109.68 1236.14,109.445 1238.3,109.212 1240.45,108.981 1242.61,108.753 1244.76,108.527 1246.92,108.303 1249.07,108.082 1251.23,107.863 1253.39,107.645 \n",
       "  1255.54,107.431 1257.7,107.218 1259.85,107.007 1262.01,106.798 1264.16,106.592 1266.32,106.388 1268.47,106.185 1270.63,105.985 1272.79,105.786 1274.94,105.59 \n",
       "  1277.1,105.395 1279.25,105.203 1281.41,105.012 1283.56,104.824 1285.72,104.637 1287.88,104.452 1290.03,104.269 1292.19,104.088 1294.34,103.908 1296.5,103.73 \n",
       "  1298.65,103.554 1300.81,103.38 1302.96,103.208 1305.12,103.037 1307.28,102.868 1309.43,102.701 1311.59,102.535 1313.74,102.371 1315.9,102.209 1318.05,102.048 \n",
       "  1320.21,101.889 1322.37,101.731 1324.52,101.575 1326.68,101.42 1328.83,101.268 1330.99,101.116 1333.14,100.966 1335.3,100.818 1337.45,100.671 1339.61,100.525 \n",
       "  1341.77,100.381 1343.92,100.238 1346.08,100.097 1348.23,99.9573 1350.39,99.8188 1352.54,99.6817 1354.7,99.546 1356.86,99.4117 1359.01,99.2786 1361.17,99.1469 \n",
       "  1363.32,99.0165 1365.48,98.8874 1367.63,98.7596 1369.79,98.6331 1371.95,98.5078 1374.1,98.3838 1376.26,98.261 1378.41,98.1395 1380.57,98.0191 1382.72,97.9 \n",
       "  1384.88,97.782 1387.03,97.6652 1389.19,97.5496 1391.35,97.4352 1393.5,97.3218 1395.66,97.2097 1397.81,97.0986 1399.97,96.9886 1402.12,96.8798 1404.28,96.772 \n",
       "  1406.44,96.6653 1408.59,96.5597 1410.75,96.4551 1412.9,96.3516 1415.06,96.2491 1417.21,96.1476 1419.37,96.0472 1421.52,95.9477 1423.68,95.8493 1425.84,95.7518 \n",
       "  1427.99,95.6553 1430.15,95.5598 1432.3,95.4652 1434.46,95.3715 1436.61,95.2788 1438.77,95.187 1440.93,95.0961 1443.08,95.0062 1445.24,94.9171 1447.39,94.8289 \n",
       "  1449.55,94.7416 1451.7,94.6552 1453.86,94.5696 1456.01,94.4848 1458.17,94.4009 1460.33,94.3179 1462.48,94.2357 1464.64,94.1542 1466.79,94.0736 1468.95,93.9938 \n",
       "  1471.1,93.9148 1473.26,93.8366 1475.42,93.7591 1477.57,93.6824 1479.73,93.6065 1481.88,93.5313 1484.04,93.4568 1486.19,93.3831 1488.35,93.3102 1490.5,93.2379 \n",
       "  1492.66,93.1664 1494.82,93.0955 1496.97,93.0254 1499.13,92.956 1501.28,92.8873 1503.44,92.8192 1505.59,92.7518 1507.75,92.6851 1509.91,92.6191 1512.06,92.5537 \n",
       "  1514.22,92.489 1516.37,92.4249 1518.53,92.3614 1520.68,92.2986 1522.84,92.2364 1524.99,92.1748 1527.15,92.1139 1529.31,92.0535 1531.46,91.9938 1533.62,91.9346 \n",
       "  1535.77,91.8761 1537.93,91.8181 1540.08,91.7607 1542.24,91.7039 1544.4,91.6477 1546.55,91.592 1548.71,91.5368 1550.86,91.4822 1553.02,91.4282 1555.17,91.3747 \n",
       "  1557.33,91.3217 1559.48,91.2693 1561.64,91.2174 1563.8,91.166 1565.95,91.1151 1568.11,91.0648 1570.26,91.0149 1572.42,90.9655 1574.57,90.9167 1576.73,90.8683 \n",
       "  1578.89,90.8204 1581.04,90.7729 1583.2,90.726 1585.35,90.6795 1587.51,90.6335 1589.66,90.5879 1591.82,90.5428 1593.97,90.4981 1596.13,90.4539 1598.29,90.4102 \n",
       "  1600.44,90.3668 1602.6,90.3239 1604.75,90.2814 1606.91,90.2394 1609.06,90.1977 1611.22,90.1565 1613.38,90.1157 1615.53,90.0753 1617.69,90.0353 1619.84,89.9956 \n",
       "  1622,89.9564 1624.15,89.9176 1626.31,89.8791 1628.46,89.8411 1630.62,89.8034 1632.78,89.766 1634.93,89.7291 1637.09,89.6925 1639.24,89.6563 1641.4,89.6204 \n",
       "  1643.55,89.5849 1645.71,89.5497 1647.87,89.5149 1650.02,89.4805 1652.18,89.4463 1654.33,89.4126 1656.49,89.3791 1658.64,89.346 1660.8,89.3132 1662.95,89.2807 \n",
       "  1665.11,89.2486 1667.27,89.2168 1669.42,89.1853 1671.58,89.1541 1673.73,89.1232 1675.89,89.0926 1678.04,89.0624 1680.2,89.0324 1682.36,89.0027 1684.51,88.9734 \n",
       "  1686.67,88.9443 1688.82,88.9155 1690.98,88.887 1693.13,88.8588 1695.29,88.8309 1697.44,88.8032 1699.6,88.7759 1701.76,88.7488 1703.91,88.7219 1706.07,88.6954 \n",
       "  1708.22,88.6691 1710.38,88.643 1712.53,88.6173 1714.69,88.5918 1716.85,88.5665 1719,88.5415 1721.16,88.5167 1723.31,88.4922 1725.47,88.468 1727.62,88.444 \n",
       "  1729.78,88.4202 1731.93,88.3966 1734.09,88.3733 1736.25,88.3502 1738.4,88.3274 1740.56,88.3048 1742.71,88.2824 1744.87,88.2602 1747.02,88.2383 1749.18,88.2166 \n",
       "  1751.34,88.1951 1753.49,88.1738 1755.65,88.1527 1757.8,88.1318 1759.96,88.1111 1762.11,88.0907 1764.27,88.0704 1766.42,88.0504 1768.58,88.0305 1770.74,88.0108 \n",
       "  1772.89,87.9914 1775.05,87.9721 1777.2,87.953 1779.36,87.9341 1781.51,87.9154 1783.67,87.8969 1785.83,87.8786 1787.98,87.8604 1790.14,87.8424 1792.29,87.8246 \n",
       "  1794.45,87.807 1796.6,87.7896 1798.76,87.7723 1800.92,87.7552 1803.07,87.7383 1805.23,87.7215 1807.38,87.7049 1809.54,87.6884 1811.69,87.6722 1813.85,87.6561 \n",
       "  1816,87.6401 1818.16,87.6243 1820.32,87.6087 1822.47,87.5932 1824.63,87.5778 1826.78,87.5627 1828.94,87.5476 1831.09,87.5328 1833.25,87.518 1835.41,87.5035 \n",
       "  1837.56,87.489 1839.72,87.4747 1841.87,87.4606 1844.03,87.4466 1846.18,87.4327 1848.34,87.419 1850.49,87.4054 1852.65,87.3919 1854.81,87.3786 1856.96,87.3654 \n",
       "  1859.12,87.3524 1861.27,87.3394 1863.43,87.3266 1865.58,87.314 1867.74,87.3014 1869.9,87.289 1872.05,87.2767 1874.21,87.2645 1876.36,87.2525 1878.52,87.2406 \n",
       "  1880.67,87.2288 1882.83,87.2171 1884.98,87.2055 1887.14,87.194 1889.3,87.1827 1891.45,87.1715 1893.61,87.1603 1895.76,87.1493 1897.92,87.1384 1900.07,87.1277 \n",
       "  1902.23,87.117 1904.39,87.1064 1906.54,87.0959 1908.7,87.0856 1910.85,87.0753 1913.01,87.0652 1915.16,87.0551 1917.32,87.0452 1919.47,87.0353 1921.63,87.0255 \n",
       "  1923.79,87.0159 1925.94,87.0063 1928.1,86.9969 1930.25,86.9875 1932.41,86.9782 1934.56,86.969 1936.72,86.9599 1938.88,86.9509 1941.03,86.942 1943.19,86.9332 \n",
       "  1945.34,86.9244 1947.5,86.9158 1949.65,86.9072 1951.81,86.8987 1953.96,86.8903 1956.12,86.882 1958.28,86.8737 1960.43,86.8656 1962.59,86.8575 1964.74,86.8495 \n",
       "  1966.9,86.8416 1969.05,86.8337 1971.21,86.826 1973.37,86.8183 1975.52,86.8107 1977.68,86.8032 1979.83,86.7957 1981.99,86.7883 1984.14,86.781 1986.3,86.7738 \n",
       "  1988.45,86.7666 1990.61,86.7595 1992.77,86.7525 1994.92,86.7455 1997.08,86.7386 1999.23,86.7318 2001.39,86.7251 2003.54,86.7184 2005.7,86.7118 2007.86,86.7052 \n",
       "  2010.01,86.6987 2012.17,86.6923 2014.32,86.686 2016.48,86.6797 2018.63,86.6734 2020.79,86.6673 2022.94,86.6612 2025.1,86.6551 2027.26,86.6491 2029.41,86.6432 \n",
       "  2031.57,86.6373 2033.72,86.6315 2035.88,86.6258 2038.03,86.6201 2040.19,86.6145 2042.35,86.6089 2044.5,86.6034 2046.66,86.5979 2048.81,86.5925 2050.97,86.5871 \n",
       "  2053.12,86.5818 2055.28,86.5766 2057.43,86.5714 2059.59,86.5662 2061.75,86.5611 2063.9,86.5561 2066.06,86.5511 2068.21,86.5462 2070.37,86.5413 2072.52,86.5364 \n",
       "  2074.68,86.5316 2076.84,86.5269 2078.99,86.5222 2081.15,86.5175 2083.3,86.5129 2085.46,86.5084 2087.61,86.5039 2089.77,86.4994 2091.92,86.495 2094.08,86.4906 \n",
       "  2096.24,86.4862 2098.39,86.4819 2100.55,86.4777 2102.7,86.4735 2104.86,86.4693 2107.01,86.4652 2109.17,86.4611 2111.33,86.4571 2113.48,86.453 2115.64,86.4491 \n",
       "  2117.79,86.4452 2119.95,86.4413 2122.1,86.4374 2124.26,86.4336 2126.41,86.4298 2128.57,86.4261 2130.73,86.4224 2132.88,86.4187 2135.04,86.4151 2137.19,86.4115 \n",
       "  2139.35,86.4079 2141.5,86.4044 2143.66,86.4009 2145.82,86.3975 2147.97,86.3941 2150.13,86.3907 2152.28,86.3873 2154.44,86.384 2156.59,86.3807 2158.75,86.3775 \n",
       "  2160.9,86.3743 2163.06,86.3711 2165.22,86.3679 2167.37,86.3648 2169.53,86.3617 2171.68,86.3586 2173.84,86.3556 2175.99,86.3526 2178.15,86.3496 2180.31,86.3467 \n",
       "  2182.46,86.3438 2184.62,86.3409 2186.77,86.338 2188.93,86.3352 2191.08,86.3324 2193.24,86.3296 2195.4,86.3269 2197.55,86.3242 2199.71,86.3215 2201.86,86.3188 \n",
       "  2204.02,86.3162 2206.17,86.3136 2208.33,86.311 2210.48,86.3085 2212.64,86.3059 2214.8,86.3034 2216.95,86.3009 2219.11,86.2985 2221.26,86.2961 2223.42,86.2936 \n",
       "  2225.57,86.2913 2227.73,86.2889 2229.89,86.2866 2232.04,86.2843 2234.2,86.282 2236.35,86.2797 2238.51,86.2775 2240.66,86.2752 2242.82,86.2731 2244.97,86.2709 \n",
       "  2247.13,86.2687 2249.29,86.2666 2251.44,86.2645 2253.6,86.2624 2255.75,86.2603 2257.91,86.2583 2260.06,86.2562 2262.22,86.2542 2264.38,86.2522 2266.53,86.2503 \n",
       "  2268.69,86.2483 2270.84,86.2464 2273,86.2445 2275.15,86.2426 2277.31,86.2407 2279.46,86.2389 2281.62,86.237 2283.78,86.2352 2285.93,86.2334 2288.09,86.2316 \n",
       "  2290.24,86.2299 2292.4,86.2281 2294.55,86.2264 2296.71,86.2247 2298.87,86.223 2301.02,86.2213 2303.18,86.2197 2305.33,86.218 2307.49,86.2164 2309.64,86.2148 \n",
       "  2311.8,86.2132 2313.95,86.2116 2316.11,86.21 2318.27,86.2085 2320.42,86.2069 2322.58,86.2054 2324.73,86.2039 2326.89,86.2024 2329.04,86.201 2331.2,86.1995 \n",
       "  2333.36,86.198 2335.51,86.1966 2337.67,86.1952 2339.82,86.1938 2341.98,86.1924 2344.13,86.191 2346.29,86.1897 2348.44,86.1883 2350.6,86.187 2352.76,86.1857 \n",
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      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "initialState = LVector(S=999, I=1, R=0);\n",
    "params = LVector(inf=0.002, rec=0.2);\n",
    "prob = ODEProblem(vectorfield(sirLabeled),initialState,(0.0,50.0),params);\n",
    "sol = solve(prob,Tsit5(),abstol=1e-8);\n",
    "plot(sol)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "1664aa9b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div class=\"c-set\">\n",
       "<span class=\"c-set-summary\">LabelledPetriNet with elements T = 1:2, S = 1:3, I = 1:3, O = 1:3</span>\n",
       "<table>\n",
       "  <thead>\n",
       "    <tr class = \"header headerLastRow\">\n",
       "      <th class = \"rowNumber\">T</th>\n",
       "      <th style = \"text-align: right;\">tname</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td class = \"rowNumber\">1</td>\n",
       "      <td style = \"text-align: right;\">inf</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td class = \"rowNumber\">2</td>\n",
       "      <td style = \"text-align: right;\">rec</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<table>\n",
       "  <thead>\n",
       "    <tr class = \"header headerLastRow\">\n",
       "      <th class = \"rowNumber\">S</th>\n",
       "      <th style = \"text-align: right;\">sname</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td class = \"rowNumber\">1</td>\n",
       "      <td style = \"text-align: right;\">S_S</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td class = \"rowNumber\">2</td>\n",
       "      <td style = \"text-align: right;\">S_I</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td class = \"rowNumber\">3</td>\n",
       "      <td style = \"text-align: right;\">S_R</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<table>\n",
       "  <thead>\n",
       "    <tr class = \"header headerLastRow\">\n",
       "      <th class = \"rowNumber\">I</th>\n",
       "      <th style = \"text-align: right;\">it</th>\n",
       "      <th style = \"text-align: right;\">is</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td class = \"rowNumber\">1</td>\n",
       "      <td style = \"text-align: right;\">1</td>\n",
       "      <td style = \"text-align: right;\">1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td class = \"rowNumber\">2</td>\n",
       "      <td style = \"text-align: right;\">1</td>\n",
       "      <td style = \"text-align: right;\">2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td class = \"rowNumber\">3</td>\n",
       "      <td style = \"text-align: right;\">2</td>\n",
       "      <td style = \"text-align: right;\">2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<table>\n",
       "  <thead>\n",
       "    <tr class = \"header headerLastRow\">\n",
       "      <th class = \"rowNumber\">O</th>\n",
       "      <th style = \"text-align: right;\">ot</th>\n",
       "      <th style = \"text-align: right;\">os</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td class = \"rowNumber\">1</td>\n",
       "      <td style = \"text-align: right;\">1</td>\n",
       "      <td style = \"text-align: right;\">2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td class = \"rowNumber\">2</td>\n",
       "      <td style = \"text-align: right;\">1</td>\n",
       "      <td style = \"text-align: right;\">2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td class = \"rowNumber\">3</td>\n",
       "      <td style = \"text-align: right;\">2</td>\n",
       "      <td style = \"text-align: right;\">3</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>\n"
      ],
      "text/plain": [
       "LabelledPetriNet with elements T = 1:2, S = 1:3, I = 1:3, O = 1:3\n",
       "┌───┬───────┐\n",
       "│\u001b[1m T \u001b[0m│\u001b[1m tname \u001b[0m│\n",
       "├───┼───────┤\n",
       "│ 1 │   inf │\n",
       "│ 2 │   rec │\n",
       "└───┴───────┘\n",
       "┌───┬───────┐\n",
       "│\u001b[1m S \u001b[0m│\u001b[1m sname \u001b[0m│\n",
       "├───┼───────┤\n",
       "│ 1 │   S_S │\n",
       "│ 2 │   S_I │\n",
       "│ 3 │   S_R │\n",
       "└───┴───────┘\n",
       "┌───┬────┬────┐\n",
       "│\u001b[1m I \u001b[0m│\u001b[1m it \u001b[0m│\u001b[1m is \u001b[0m│\n",
       "├───┼────┼────┤\n",
       "│ 1 │  1 │  1 │\n",
       "│ 2 │  1 │  2 │\n",
       "│ 3 │  2 │  2 │\n",
       "└───┴────┴────┘\n",
       "┌───┬────┬────┐\n",
       "│\u001b[1m O \u001b[0m│\u001b[1m ot \u001b[0m│\u001b[1m os \u001b[0m│\n",
       "├───┼────┼────┤\n",
       "│ 1 │  1 │  2 │\n",
       "│ 2 │  1 │  2 │\n",
       "│ 3 │  2 │  3 │\n",
       "└───┴────┴────┘\n"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sirLabeledDisambiguated = LabelledPetriNet([:S_S, :S_I, :S_R], :inf=>((:S_S,:S_I)=>(:S_I,:S_I)), :rec=>(:S_I=>:S_R))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "57f87527",
   "metadata": {},
   "outputs": [
    {
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       "Graph(\"G\", true, \"dot\", Catlab.Graphics.Graphviz.Statement[Catlab.Graphics.Graphviz.Node(\"s1\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"S_S\", :shape => \"circle\", :color => \"#6C9AC3\", :pos => \"\")), Catlab.Graphics.Graphviz.Node(\"s2\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"S_I\", :shape => \"circle\", :color => \"#6C9AC3\", :pos => \"\")), Catlab.Graphics.Graphviz.Node(\"s3\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"S_R\", :shape => \"circle\", :color => \"#6C9AC3\", :pos => \"\")), Catlab.Graphics.Graphviz.Node(\"t1\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"inf\", :shape => \"square\", :color => \"#E28F41\", :pos => \"\")), Catlab.Graphics.Graphviz.Node(\"t2\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"rec\", :shape => \"square\", :color => \"#E28F41\", :pos => \"\")), Catlab.Graphics.Graphviz.Edge(Catlab.Graphics.Graphviz.NodeID[Catlab.Graphics.Graphviz.NodeID(\"s2\", \"\", \"\"), Catlab.Graphics.Graphviz.NodeID(\"t2\", \"\", \"\")], OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:labelfontsize => \"6\", :label => \"1\")), Catlab.Graphics.Graphviz.Edge(Catlab.Graphics.Graphviz.NodeID[Catlab.Graphics.Graphviz.NodeID(\"t2\", \"\", \"\"), Catlab.Graphics.Graphviz.NodeID(\"s3\", \"\", \"\")], OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:labelfontsize => \"6\", :label => \"1\")), Catlab.Graphics.Graphviz.Edge(Catlab.Graphics.Graphviz.NodeID[Catlab.Graphics.Graphviz.NodeID(\"t1\", \"\", \"\"), Catlab.Graphics.Graphviz.NodeID(\"s2\", \"\", \"\")], OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:labelfontsize => \"6\", :label => \"2\")), Catlab.Graphics.Graphviz.Edge(Catlab.Graphics.Graphviz.NodeID[Catlab.Graphics.Graphviz.NodeID(\"s2\", \"\", \"\"), Catlab.Graphics.Graphviz.NodeID(\"t1\", \"\", \"\")], OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:labelfontsize => \"6\", :label => \"1\")), Catlab.Graphics.Graphviz.Edge(Catlab.Graphics.Graphviz.NodeID[Catlab.Graphics.Graphviz.NodeID(\"s1\", \"\", \"\"), Catlab.Graphics.Graphviz.NodeID(\"t1\", \"\", \"\")], OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:labelfontsize => \"6\", :label => \"1\"))], OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:rankdir => \"LR\"), OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:shape => \"plain\", :style => \"filled\", :color => \"white\"), OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:splines => \"splines\"))"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Graph(sirLabeledDisambiguated)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "b865c016",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<div class=\"c-set\">\n",
       "<span class=\"c-set-summary\">LabelledPetriNet with elements T = 1:3, S = 1:3, I = 1:4, O = 1:4</span>\n",
       "<table>\n",
       "  <thead>\n",
       "    <tr class = \"header headerLastRow\">\n",
       "      <th class = \"rowNumber\">T</th>\n",
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      "text/plain": [
       "LabelledPetriNet with elements T = 1:3, S = 1:3, I = 1:4, O = 1:4\n",
       "┌───┬────────┐\n",
       "│\u001b[1m T \u001b[0m│\u001b[1m  tname \u001b[0m│\n",
       "├───┼────────┤\n",
       "│ 1 │    inf │\n",
       "│ 2 │    rec │\n",
       "│ 3 │ waning │\n",
       "└───┴────────┘\n",
       "┌───┬───────┐\n",
       "│\u001b[1m S \u001b[0m│\u001b[1m sname \u001b[0m│\n",
       "├───┼───────┤\n",
       "│ 1 │   S_S │\n",
       "│ 2 │   S_I │\n",
       "│ 3 │   S_R │\n",
       "└───┴───────┘\n",
       "┌───┬────┬────┐\n",
       "│\u001b[1m I \u001b[0m│\u001b[1m it \u001b[0m│\u001b[1m is \u001b[0m│\n",
       "├───┼────┼────┤\n",
       "│ 1 │  1 │  1 │\n",
       "│ 2 │  1 │  2 │\n",
       "│ 3 │  2 │  2 │\n",
       "│ 4 │  3 │  3 │\n",
       "└───┴────┴────┘\n",
       "┌───┬────┬────┐\n",
       "│\u001b[1m O \u001b[0m│\u001b[1m ot \u001b[0m│\u001b[1m os \u001b[0m│\n",
       "├───┼────┼────┤\n",
       "│ 1 │  1 │  2 │\n",
       "│ 2 │  1 │  2 │\n",
       "│ 3 │  2 │  3 │\n",
       "│ 4 │  3 │  1 │\n",
       "└───┴────┴────┘\n"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sirsLabeledDisambiguated = LabelledPetriNet([:S_S, :S_I, :S_R], :inf=>((:S_S,:S_I)=>(:S_I,:S_I)), :rec=>(:S_I=>:S_R), :waning=>(:S_R=>:S_S))"
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  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "eaa0135d",
   "metadata": {},
   "outputs": [
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      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Graph(sirsLabeledDisambiguated)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "d4e36a03",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<div class=\"c-set\">\n",
       "<span class=\"c-set-summary\">LabelledPetriNet with elements T = 1:2, S = 1:4, I = 1:4, O = 1:4</span>\n",
       "<table>\n",
       "  <thead>\n",
       "    <tr class = \"header headerLastRow\">\n",
       "      <th class = \"rowNumber\">T</th>\n",
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       "      <td class = \"rowNumber\">2</td>\n",
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       "  <thead>\n",
       "    <tr class = \"header headerLastRow\">\n",
       "      <th class = \"rowNumber\">S</th>\n",
       "      <th style = \"text-align: right;\">sname</th>\n",
       "    </tr>\n",
       "  </thead>\n",
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       "      <td class = \"rowNumber\">1</td>\n",
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       "      <td class = \"rowNumber\">2</td>\n",
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       "      <td class = \"rowNumber\">3</td>\n",
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       "    <tr>\n",
       "      <td class = \"rowNumber\">4</td>\n",
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       "<table>\n",
       "  <thead>\n",
       "    <tr class = \"header headerLastRow\">\n",
       "      <th class = \"rowNumber\">I</th>\n",
       "      <th style = \"text-align: right;\">it</th>\n",
       "      <th style = \"text-align: right;\">is</th>\n",
       "    </tr>\n",
       "  </thead>\n",
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       "      <td class = \"rowNumber\">1</td>\n",
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       "    <tr>\n",
       "      <td class = \"rowNumber\">3</td>\n",
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      "text/plain": [
       "LabelledPetriNet with elements T = 1:2, S = 1:4, I = 1:4, O = 1:4\n",
       "┌───┬───────┐\n",
       "│\u001b[1m T \u001b[0m│\u001b[1m tname \u001b[0m│\n",
       "├───┼───────┤\n",
       "│ 1 │   inf │\n",
       "│ 2 │   rec │\n",
       "└───┴───────┘\n",
       "┌───┬───────┐\n",
       "│\u001b[1m S \u001b[0m│\u001b[1m sname \u001b[0m│\n",
       "├───┼───────┤\n",
       "│ 1 │   S_S │\n",
       "│ 2 │   S_I │\n",
       "│ 3 │   S_R │\n",
       "│ 4 │   S_H │\n",
       "└───┴───────┘\n",
       "┌───┬────┬────┐\n",
       "│\u001b[1m I \u001b[0m│\u001b[1m it \u001b[0m│\u001b[1m is \u001b[0m│\n",
       "├───┼────┼────┤\n",
       "│ 1 │  1 │  1 │\n",
       "│ 2 │  1 │  2 │\n",
       "│ 3 │  2 │  2 │\n",
       "│ 4 │  2 │  4 │\n",
       "└───┴────┴────┘\n",
       "┌───┬────┬────┐\n",
       "│\u001b[1m O \u001b[0m│\u001b[1m ot \u001b[0m│\u001b[1m os \u001b[0m│\n",
       "├───┼────┼────┤\n",
       "│ 1 │  1 │  2 │\n",
       "│ 2 │  1 │  2 │\n",
       "│ 3 │  2 │  3 │\n",
       "│ 4 │  2 │  4 │\n",
       "└───┴────┴────┘\n"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sirTreatmentMediatedLabeledDisambiguated = LabelledPetriNet([:S_S, :S_I, :S_R, :S_H], :inf=>((:S_S,:S_I)=>(:S_I,:S_I)), :rec=>((:S_I,:S_H)=>(:S_R,:S_H)))"
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  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "32e194c5",
   "metadata": {},
   "outputs": [
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      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Graph(sirTreatmentMediatedLabeledDisambiguated)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "301c0625",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<div class=\"c-set\">\n",
       "<span class=\"c-set-summary\">LabelledPetriNet with elements T = 1:3, S = 1:4, I = 1:4, O = 1:4</span>\n",
       "<table>\n",
       "  <thead>\n",
       "    <tr class = \"header headerLastRow\">\n",
       "      <th class = \"rowNumber\">T</th>\n",
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       "  </thead>\n",
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       "      <td class = \"rowNumber\">1</td>\n",
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       "      <td class = \"rowNumber\">2</td>\n",
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       "    <tr>\n",
       "      <td class = \"rowNumber\">3</td>\n",
       "      <td style = \"text-align: right;\">rec</td>\n",
       "    </tr>\n",
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       "  <thead>\n",
       "    <tr class = \"header headerLastRow\">\n",
       "      <th class = \"rowNumber\">S</th>\n",
       "      <th style = \"text-align: right;\">sname</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td class = \"rowNumber\">1</td>\n",
       "      <td style = \"text-align: right;\">S_S</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td class = \"rowNumber\">2</td>\n",
       "      <td style = \"text-align: right;\">S_E</td>\n",
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       "    <tr>\n",
       "      <td class = \"rowNumber\">3</td>\n",
       "      <td style = \"text-align: right;\">S_I</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td class = \"rowNumber\">4</td>\n",
       "      <td style = \"text-align: right;\">S_R</td>\n",
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       "  </tbody>\n",
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       "<table>\n",
       "  <thead>\n",
       "    <tr class = \"header headerLastRow\">\n",
       "      <th class = \"rowNumber\">I</th>\n",
       "      <th style = \"text-align: right;\">it</th>\n",
       "      <th style = \"text-align: right;\">is</th>\n",
       "    </tr>\n",
       "  </thead>\n",
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       "      <td style = \"text-align: right;\">1</td>\n",
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       "      <td style = \"text-align: right;\">3</td>\n",
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       "      <td style = \"text-align: right;\">2</td>\n",
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       "      <td style = \"text-align: right;\">3</td>\n",
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       "      <td style = \"text-align: right;\">4</td>\n",
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      "text/plain": [
       "LabelledPetriNet with elements T = 1:3, S = 1:4, I = 1:4, O = 1:4\n",
       "┌───┬─────────┐\n",
       "│\u001b[1m T \u001b[0m│\u001b[1m   tname \u001b[0m│\n",
       "├───┼─────────┤\n",
       "│ 1 │     inf │\n",
       "│ 2 │ postLat │\n",
       "│ 3 │     rec │\n",
       "└───┴─────────┘\n",
       "┌───┬───────┐\n",
       "│\u001b[1m S \u001b[0m│\u001b[1m sname \u001b[0m│\n",
       "├───┼───────┤\n",
       "│ 1 │   S_S │\n",
       "│ 2 │   S_E │\n",
       "│ 3 │   S_I │\n",
       "│ 4 │   S_R │\n",
       "└───┴───────┘\n",
       "┌───┬────┬────┐\n",
       "│\u001b[1m I \u001b[0m│\u001b[1m it \u001b[0m│\u001b[1m is \u001b[0m│\n",
       "├───┼────┼────┤\n",
       "│ 1 │  1 │  1 │\n",
       "│ 2 │  1 │  3 │\n",
       "│ 3 │  2 │  2 │\n",
       "│ 4 │  3 │  3 │\n",
       "└───┴────┴────┘\n",
       "┌───┬────┬────┐\n",
       "│\u001b[1m O \u001b[0m│\u001b[1m ot \u001b[0m│\u001b[1m os \u001b[0m│\n",
       "├───┼────┼────┤\n",
       "│ 1 │  1 │  2 │\n",
       "│ 2 │  1 │  3 │\n",
       "│ 3 │  2 │  3 │\n",
       "│ 4 │  3 │  4 │\n",
       "└───┴────┴────┘\n"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "seirLabeled = LabelledPetriNet([:S_S, :S_E, :S_I, :S_R], :inf=>((:S_S,:S_I)=>(:S_E,:S_I)), :postLat=>(:S_E=>:S_I), :rec=>(:S_I=>:S_R))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "05df0d3d",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
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      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Graph(seirLabeled)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "id": "edd7aba4",
   "metadata": {},
   "outputs": [
    {
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       "<div class=\"c-set\">\n",
       "<span class=\"c-set-summary\">LabelledPetriNet with elements T = 1:5, S = 1:5, I = 1:6, O = 1:6</span>\n",
       "<table>\n",
       "  <thead>\n",
       "    <tr class = \"header headerLastRow\">\n",
       "      <th class = \"rowNumber\">T</th>\n",
       "      <th style = \"text-align: right;\">tname</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td class = \"rowNumber\">1</td>\n",
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       "    <tr>\n",
       "      <td class = \"rowNumber\">2</td>\n",
       "      <td style = \"text-align: right;\">symp</td>\n",
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       "    <tr>\n",
       "      <td class = \"rowNumber\">3</td>\n",
       "      <td style = \"text-align: right;\">asymp</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td class = \"rowNumber\">4</td>\n",
       "      <td style = \"text-align: right;\">recS</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td class = \"rowNumber\">5</td>\n",
       "      <td style = \"text-align: right;\">recA</td>\n",
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       "  </tbody>\n",
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       "<table>\n",
       "  <thead>\n",
       "    <tr class = \"header headerLastRow\">\n",
       "      <th class = \"rowNumber\">S</th>\n",
       "      <th style = \"text-align: right;\">sname</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td class = \"rowNumber\">1</td>\n",
       "      <td style = \"text-align: right;\">S</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td class = \"rowNumber\">2</td>\n",
       "      <td style = \"text-align: right;\">E</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td class = \"rowNumber\">3</td>\n",
       "      <td style = \"text-align: right;\">I</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td class = \"rowNumber\">4</td>\n",
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       "    </tr>\n",
       "    <tr>\n",
       "      <td class = \"rowNumber\">5</td>\n",
       "      <td style = \"text-align: right;\">R</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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       "<table>\n",
       "  <thead>\n",
       "    <tr class = \"header headerLastRow\">\n",
       "      <th class = \"rowNumber\">I</th>\n",
       "      <th style = \"text-align: right;\">it</th>\n",
       "      <th style = \"text-align: right;\">is</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td class = \"rowNumber\">1</td>\n",
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       "    <tr>\n",
       "      <td class = \"rowNumber\">3</td>\n",
       "      <td style = \"text-align: right;\">2</td>\n",
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       "      <td style = \"text-align: right;\">3</td>\n",
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       "  <thead>\n",
       "    <tr class = \"header headerLastRow\">\n",
       "      <th class = \"rowNumber\">O</th>\n",
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      "text/plain": [
       "LabelledPetriNet with elements T = 1:5, S = 1:5, I = 1:6, O = 1:6\n",
       "┌───┬───────┐\n",
       "│\u001b[1m T \u001b[0m│\u001b[1m tname \u001b[0m│\n",
       "├───┼───────┤\n",
       "│ 1 │   inf │\n",
       "│ 2 │  symp │\n",
       "│ 3 │ asymp │\n",
       "│ 4 │  recS │\n",
       "│ 5 │  recA │\n",
       "└───┴───────┘\n",
       "┌───┬───────┐\n",
       "│\u001b[1m S \u001b[0m│\u001b[1m sname \u001b[0m│\n",
       "├───┼───────┤\n",
       "│ 1 │     S │\n",
       "│ 2 │     E │\n",
       "│ 3 │     I │\n",
       "│ 4 │     A │\n",
       "│ 5 │     R │\n",
       "└───┴───────┘\n",
       "┌───┬────┬────┐\n",
       "│\u001b[1m I \u001b[0m│\u001b[1m it \u001b[0m│\u001b[1m is \u001b[0m│\n",
       "├───┼────┼────┤\n",
       "│ 1 │  1 │  1 │\n",
       "│ 2 │  1 │  3 │\n",
       "│ 3 │  2 │  2 │\n",
       "│ 4 │  3 │  2 │\n",
       "│ 5 │  4 │  3 │\n",
       "│ 6 │  5 │  4 │\n",
       "└───┴────┴────┘\n",
       "┌───┬────┬────┐\n",
       "│\u001b[1m O \u001b[0m│\u001b[1m ot \u001b[0m│\u001b[1m os \u001b[0m│\n",
       "├───┼────┼────┤\n",
       "│ 1 │  1 │  2 │\n",
       "│ 2 │  1 │  3 │\n",
       "│ 3 │  2 │  3 │\n",
       "│ 4 │  3 │  4 │\n",
       "│ 5 │  4 │  5 │\n",
       "│ 6 │  5 │  5 │\n",
       "└───┴────┴────┘\n"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "seiarLabeled = LabelledPetriNet([:S, :E, :I, :A, :R], :inf=>((:S,:I)=>(:E,:I)), :symp=>(:E=>:I), :asymp=>(:E=>:A), :recS=>(:I=>:R), :recA=>(:A=>:R))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "id": "44b927c8",
   "metadata": {},
   "outputs": [
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      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Graph(seiarLabeled)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "52e7a2f9",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<div class=\"c-set\">\n",
       "<span class=\"c-set-summary\">LabelledPetriNet with elements T = 1:4, S = 1:4, I = 1:5, O = 1:5</span>\n",
       "<table>\n",
       "  <thead>\n",
       "    <tr class = \"header headerLastRow\">\n",
       "      <th class = \"rowNumber\">T</th>\n",
       "      <th style = \"text-align: right;\">tname</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td class = \"rowNumber\">1</td>\n",
       "      <td style = \"text-align: right;\">inf</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td class = \"rowNumber\">2</td>\n",
       "      <td style = \"text-align: right;\">postLatency</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td class = \"rowNumber\">3</td>\n",
       "      <td style = \"text-align: right;\">rec</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td class = \"rowNumber\">4</td>\n",
       "      <td style = \"text-align: right;\">waning</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<table>\n",
       "  <thead>\n",
       "    <tr class = \"header headerLastRow\">\n",
       "      <th class = \"rowNumber\">S</th>\n",
       "      <th style = \"text-align: right;\">sname</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td class = \"rowNumber\">1</td>\n",
       "      <td style = \"text-align: right;\">S</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td class = \"rowNumber\">2</td>\n",
       "      <td style = \"text-align: right;\">E</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td class = \"rowNumber\">3</td>\n",
       "      <td style = \"text-align: right;\">I</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td class = \"rowNumber\">4</td>\n",
       "      <td style = \"text-align: right;\">R</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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       "<table>\n",
       "  <thead>\n",
       "    <tr class = \"header headerLastRow\">\n",
       "      <th class = \"rowNumber\">I</th>\n",
       "      <th style = \"text-align: right;\">it</th>\n",
       "      <th style = \"text-align: right;\">is</th>\n",
       "    </tr>\n",
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       "  <tbody>\n",
       "    <tr>\n",
       "      <td class = \"rowNumber\">1</td>\n",
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       "      <td style = \"text-align: right;\">1</td>\n",
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       "      <td style = \"text-align: right;\">3</td>\n",
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       "    <tr>\n",
       "      <td class = \"rowNumber\">4</td>\n",
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       "      <td class = \"rowNumber\">5</td>\n",
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       "<table>\n",
       "  <thead>\n",
       "    <tr class = \"header headerLastRow\">\n",
       "      <th class = \"rowNumber\">O</th>\n",
       "      <th style = \"text-align: right;\">ot</th>\n",
       "      <th style = \"text-align: right;\">os</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td class = \"rowNumber\">1</td>\n",
       "      <td style = \"text-align: right;\">1</td>\n",
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       "      <td style = \"text-align: right;\">3</td>\n",
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       "    <tr>\n",
       "      <td class = \"rowNumber\">3</td>\n",
       "      <td style = \"text-align: right;\">2</td>\n",
       "      <td style = \"text-align: right;\">3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td class = \"rowNumber\">4</td>\n",
       "      <td style = \"text-align: right;\">3</td>\n",
       "      <td style = \"text-align: right;\">4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td class = \"rowNumber\">5</td>\n",
       "      <td style = \"text-align: right;\">4</td>\n",
       "      <td style = \"text-align: right;\">1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>\n"
      ],
      "text/plain": [
       "LabelledPetriNet with elements T = 1:4, S = 1:4, I = 1:5, O = 1:5\n",
       "┌───┬─────────────┐\n",
       "│\u001b[1m T \u001b[0m│\u001b[1m       tname \u001b[0m│\n",
       "├───┼─────────────┤\n",
       "│ 1 │         inf │\n",
       "│ 2 │ postLatency │\n",
       "│ 3 │         rec │\n",
       "│ 4 │      waning │\n",
       "└───┴─────────────┘\n",
       "┌───┬───────┐\n",
       "│\u001b[1m S \u001b[0m│\u001b[1m sname \u001b[0m│\n",
       "├───┼───────┤\n",
       "│ 1 │     S │\n",
       "│ 2 │     E │\n",
       "│ 3 │     I │\n",
       "│ 4 │     R │\n",
       "└───┴───────┘\n",
       "┌───┬────┬────┐\n",
       "│\u001b[1m I \u001b[0m│\u001b[1m it \u001b[0m│\u001b[1m is \u001b[0m│\n",
       "├───┼────┼────┤\n",
       "│ 1 │  1 │  1 │\n",
       "│ 2 │  1 │  3 │\n",
       "│ 3 │  2 │  2 │\n",
       "│ 4 │  3 │  3 │\n",
       "│ 5 │  4 │  4 │\n",
       "└───┴────┴────┘\n",
       "┌───┬────┬────┐\n",
       "│\u001b[1m O \u001b[0m│\u001b[1m ot \u001b[0m│\u001b[1m os \u001b[0m│\n",
       "├───┼────┼────┤\n",
       "│ 1 │  1 │  2 │\n",
       "│ 2 │  1 │  3 │\n",
       "│ 3 │  2 │  3 │\n",
       "│ 4 │  3 │  4 │\n",
       "│ 5 │  4 │  1 │\n",
       "└───┴────┴────┘\n"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "seirsLabeled = LabelledPetriNet([:S, :E, :I, :R], :inf=>((:S,:I)=>(:E,:I)), :postLatency=>(:E=>:I), :rec=>(:I=>:R), :waning=>(:R=>:S))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "7d57c726",
   "metadata": {},
   "outputs": [
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      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Graph(seirsLabeled)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "cd8f55a4",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<div class=\"c-set\">\n",
       "<span class=\"c-set-summary\">LabelledPetriNet with elements T = 1:4, S = 1:5, I = 1:6, O = 1:6</span>\n",
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       "  <thead>\n",
       "    <tr class = \"header headerLastRow\">\n",
       "      <th class = \"rowNumber\">T</th>\n",
       "      <th style = \"text-align: right;\">tname</th>\n",
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       "  </thead>\n",
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       "      <td class = \"rowNumber\">1</td>\n",
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       "      <td class = \"rowNumber\">2</td>\n",
       "      <td style = \"text-align: right;\">postLatency</td>\n",
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       "    <tr>\n",
       "      <td class = \"rowNumber\">3</td>\n",
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       "    <tr class = \"header headerLastRow\">\n",
       "      <th class = \"rowNumber\">S</th>\n",
       "      <th style = \"text-align: right;\">sname</th>\n",
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       "  <tbody>\n",
       "    <tr>\n",
       "      <td class = \"rowNumber\">1</td>\n",
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       "    <tr>\n",
       "      <td class = \"rowNumber\">2</td>\n",
       "      <td style = \"text-align: right;\">E</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td class = \"rowNumber\">3</td>\n",
       "      <td style = \"text-align: right;\">I</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td class = \"rowNumber\">4</td>\n",
       "      <td style = \"text-align: right;\">R</td>\n",
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       "    <tr>\n",
       "      <td class = \"rowNumber\">5</td>\n",
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       "  <thead>\n",
       "    <tr class = \"header headerLastRow\">\n",
       "      <th class = \"rowNumber\">I</th>\n",
       "      <th style = \"text-align: right;\">it</th>\n",
       "      <th style = \"text-align: right;\">is</th>\n",
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       "  </thead>\n",
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       "      <td class = \"rowNumber\">1</td>\n",
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       "    <tr>\n",
       "      <td class = \"rowNumber\">4</td>\n",
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       "      <td style = \"text-align: right;\">5</td>\n",
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       "      <td class = \"rowNumber\">5</td>\n",
       "      <td style = \"text-align: right;\">3</td>\n",
       "      <td style = \"text-align: right;\">3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td class = \"rowNumber\">6</td>\n",
       "      <td style = \"text-align: right;\">4</td>\n",
       "      <td style = \"text-align: right;\">4</td>\n",
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       "  </tbody>\n",
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       "<table>\n",
       "  <thead>\n",
       "    <tr class = \"header headerLastRow\">\n",
       "      <th class = \"rowNumber\">O</th>\n",
       "      <th style = \"text-align: right;\">ot</th>\n",
       "      <th style = \"text-align: right;\">os</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td class = \"rowNumber\">1</td>\n",
       "      <td style = \"text-align: right;\">1</td>\n",
       "      <td style = \"text-align: right;\">2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td class = \"rowNumber\">2</td>\n",
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       "      <td style = \"text-align: right;\">3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td class = \"rowNumber\">3</td>\n",
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       "      <td class = \"rowNumber\">4</td>\n",
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       "      <td style = \"text-align: right;\">5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td class = \"rowNumber\">5</td>\n",
       "      <td style = \"text-align: right;\">3</td>\n",
       "      <td style = \"text-align: right;\">4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td class = \"rowNumber\">6</td>\n",
       "      <td style = \"text-align: right;\">4</td>\n",
       "      <td style = \"text-align: right;\">1</td>\n",
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      "text/plain": [
       "LabelledPetriNet with elements T = 1:4, S = 1:5, I = 1:6, O = 1:6\n",
       "┌───┬─────────────┐\n",
       "│\u001b[1m T \u001b[0m│\u001b[1m       tname \u001b[0m│\n",
       "├───┼─────────────┤\n",
       "│ 1 │         inf │\n",
       "│ 2 │ postLatency │\n",
       "│ 3 │         rec │\n",
       "│ 4 │      waning │\n",
       "└───┴─────────────┘\n",
       "┌───┬───────┐\n",
       "│\u001b[1m S \u001b[0m│\u001b[1m sname \u001b[0m│\n",
       "├───┼───────┤\n",
       "│ 1 │     S │\n",
       "│ 2 │     E │\n",
       "│ 3 │     I │\n",
       "│ 4 │     R │\n",
       "│ 5 │     H │\n",
       "└───┴───────┘\n",
       "┌───┬────┬────┐\n",
       "│\u001b[1m I \u001b[0m│\u001b[1m it \u001b[0m│\u001b[1m is \u001b[0m│\n",
       "├───┼────┼────┤\n",
       "│ 1 │  1 │  1 │\n",
       "│ 2 │  1 │  3 │\n",
       "│ 3 │  2 │  2 │\n",
       "│ 4 │  3 │  5 │\n",
       "│ 5 │  3 │  3 │\n",
       "│ 6 │  4 │  4 │\n",
       "└───┴────┴────┘\n",
       "┌───┬────┬────┐\n",
       "│\u001b[1m O \u001b[0m│\u001b[1m ot \u001b[0m│\u001b[1m os \u001b[0m│\n",
       "├───┼────┼────┤\n",
       "│ 1 │  1 │  2 │\n",
       "│ 2 │  1 │  3 │\n",
       "│ 3 │  2 │  3 │\n",
       "│ 4 │  3 │  5 │\n",
       "│ 5 │  3 │  4 │\n",
       "│ 6 │  4 │  1 │\n",
       "└───┴────┴────┘\n"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "seirsTreatmentMediated = LabelledPetriNet([:S, :E, :I, :R, :H], :inf=>((:S,:I)=>(:E,:I)), :postLatency=>(:E=>:I), :rec=>((:H,:I)=>((:H,:R))), :waning=>(:R=>:S))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "f6cdb5d1",
   "metadata": {},
   "outputs": [
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     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Graph(seirsTreatmentMediated)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "2c09dd89",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "TransitionMatrices([1 0 1 0 0; 0 1 0 0 0; 0 0 1 0 1; 0 0 0 1 0], [0 1 1 0 0; 0 0 1 0 0; 0 0 0 1 1; 1 0 0 0 0])"
     ]
    }
   ],
   "source": [
    "print(TransitionMatrices(seirsTreatmentMediated))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "9374094f",
   "metadata": {
    "scrolled": false
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       "  1185.61,1254.3 1187.43,1254.29 1189.26,1254.29 1191.09,1254.29 1192.91,1254.29 1194.74,1254.3 1196.57,1254.31 1198.39,1254.31 1200.22,1254.32 1202.05,1254.32 \n",
       "  1203.87,1254.32 1205.7,1254.31 1207.52,1254.31 1209.35,1254.3 1211.18,1254.29 1213,1254.29 1214.83,1254.29 1216.66,1254.29 1218.48,1254.3 1220.31,1254.31 \n",
       "  1222.14,1254.31 1223.96,1254.32 1225.79,1254.32 1227.62,1254.31 1229.44,1254.31 1231.27,1254.3 1233.1,1254.29 1234.92,1254.29 1236.75,1254.29 1238.58,1254.29 \n",
       "  1240.4,1254.3 1242.23,1254.31 1244.06,1254.31 1245.88,1254.32 1247.71,1254.32 1249.53,1254.32 1251.36,1254.31 1253.19,1254.3 1255.01,1254.3 1256.84,1254.29 \n",
       "  1258.67,1254.29 1260.49,1254.29 1262.32,1254.29 1264.15,1254.3 1265.97,1254.31 1267.8,1254.31 1269.63,1254.32 1271.45,1254.32 1273.28,1254.31 1275.11,1254.31 \n",
       "  1276.93,1254.3 1278.76,1254.29 1280.59,1254.29 1282.41,1254.29 1284.24,1254.29 1286.07,1254.3 1287.89,1254.31 1289.72,1254.31 1291.55,1254.32 1293.37,1254.32 \n",
       "  1295.2,1254.32 1297.02,1254.31 1298.85,1254.3 1300.68,1254.3 1302.5,1254.29 1304.33,1254.29 1306.16,1254.29 1307.98,1254.29 1309.81,1254.3 1311.64,1254.31 \n",
       "  1313.46,1254.31 1315.29,1254.32 1317.12,1254.32 1318.94,1254.31 1320.77,1254.31 1322.6,1254.3 1324.42,1254.29 1326.25,1254.29 1328.08,1254.29 1329.9,1254.29 \n",
       "  1331.73,1254.3 1333.56,1254.31 1335.38,1254.31 1337.21,1254.32 1339.03,1254.32 1340.86,1254.32 1342.69,1254.31 1344.51,1254.3 1346.34,1254.3 1348.17,1254.29 \n",
       "  1349.99,1254.29 1351.82,1254.29 1353.65,1254.29 1355.47,1254.3 1357.3,1254.31 1359.13,1254.31 1360.95,1254.32 1362.78,1254.32 1364.61,1254.31 1366.43,1254.31 \n",
       "  1368.26,1254.3 1370.09,1254.29 1371.91,1254.29 1373.74,1254.29 1375.57,1254.29 1377.39,1254.3 1379.22,1254.31 1381.04,1254.31 1382.87,1254.32 1384.7,1254.32 \n",
       "  1386.52,1254.32 1388.35,1254.31 1390.18,1254.3 1392,1254.3 1393.83,1254.29 1395.66,1254.29 1397.48,1254.29 1399.31,1254.3 1401.14,1254.3 1402.96,1254.31 \n",
       "  1404.79,1254.31 1406.62,1254.32 1408.44,1254.32 1410.27,1254.31 1412.1,1254.31 1413.92,1254.3 1415.75,1254.29 1417.58,1254.29 1419.4,1254.29 1421.23,1254.29 \n",
       "  1423.05,1254.3 1424.88,1254.31 1426.71,1254.31 1428.53,1254.32 1430.36,1254.32 1432.19,1254.32 1434.01,1254.31 1435.84,1254.3 1437.67,1254.3 1439.49,1254.29 \n",
       "  1441.32,1254.29 1443.15,1254.29 1444.97,1254.3 1446.8,1254.3 1448.63,1254.31 1450.45,1254.31 1452.28,1254.32 1454.11,1254.32 1455.93,1254.31 1457.76,1254.31 \n",
       "  1459.59,1254.3 1461.41,1254.29 1463.24,1254.29 1465.06,1254.29 1466.89,1254.29 1468.72,1254.3 1470.54,1254.31 1472.37,1254.31 1474.2,1254.32 1476.02,1254.32 \n",
       "  1477.85,1254.32 1479.68,1254.31 1481.5,1254.3 1483.33,1254.3 1485.16,1254.29 1486.98,1254.29 1488.81,1254.29 1490.64,1254.3 1492.46,1254.3 1494.29,1254.31 \n",
       "  1496.12,1254.32 1497.94,1254.32 1499.77,1254.32 1501.6,1254.31 1503.42,1254.31 1505.25,1254.3 1507.07,1254.29 1508.9,1254.29 1510.73,1254.29 1512.55,1254.29 \n",
       "  1514.38,1254.3 1516.21,1254.31 1518.03,1254.31 1519.86,1254.32 1521.69,1254.32 1523.51,1254.31 1525.34,1254.31 1527.17,1254.3 1528.99,1254.3 1530.82,1254.29 \n",
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       "  1569.18,1254.31 1571,1254.31 1572.83,1254.3 1574.66,1254.3 1576.48,1254.29 1578.31,1254.29 1580.14,1254.29 1581.96,1254.3 1583.79,1254.3 1585.62,1254.31 \n",
       "  1587.44,1254.32 1589.27,1254.32 1591.1,1254.32 1592.92,1254.31 1594.75,1254.31 1596.57,1254.3 1598.4,1254.29 1600.23,1254.29 1602.05,1254.29 1603.88,1254.29 \n",
       "  1605.71,1254.3 1607.53,1254.31 1609.36,1254.31 1611.19,1254.32 1613.01,1254.32 1614.84,1254.31 1616.67,1254.31 1618.49,1254.3 1620.32,1254.3 1622.15,1254.29 \n",
       "  1623.97,1254.29 1625.8,1254.29 1627.63,1254.3 1629.45,1254.3 1631.28,1254.31 1633.11,1254.32 1634.93,1254.32 1636.76,1254.32 1638.58,1254.31 1640.41,1254.31 \n",
       "  1642.24,1254.3 1644.06,1254.29 1645.89,1254.29 1647.72,1254.29 1649.54,1254.29 1651.37,1254.3 1653.2,1254.31 1655.02,1254.31 1656.85,1254.32 1658.68,1254.32 \n",
       "  1660.5,1254.31 1662.33,1254.31 1664.16,1254.3 1665.98,1254.29 1667.81,1254.29 1669.64,1254.29 1671.46,1254.29 1673.29,1254.3 1675.12,1254.3 1676.94,1254.31 \n",
       "  1678.77,1254.32 1680.59,1254.32 1682.42,1254.32 1684.25,1254.31 1686.07,1254.31 1687.9,1254.3 1689.73,1254.29 1691.55,1254.29 1693.38,1254.29 1695.21,1254.29 \n",
       "  1697.03,1254.3 1698.86,1254.31 1700.69,1254.31 1702.51,1254.32 1704.34,1254.32 1706.17,1254.31 1707.99,1254.31 1709.82,1254.3 1711.65,1254.29 1713.47,1254.29 \n",
       "  1715.3,1254.29 1717.13,1254.29 1718.95,1254.3 1720.78,1254.3 1722.6,1254.31 1724.43,1254.32 1726.26,1254.32 1728.08,1254.32 1729.91,1254.31 1731.74,1254.31 \n",
       "  1733.56,1254.3 1735.39,1254.29 1737.22,1254.29 1739.04,1254.29 1740.87,1254.29 1742.7,1254.3 1744.52,1254.31 1746.35,1254.31 1748.18,1254.32 1750,1254.32 \n",
       "  1751.83,1254.31 1753.66,1254.31 1755.48,1254.3 1757.31,1254.29 1759.14,1254.29 1760.96,1254.29 1762.79,1254.29 1764.61,1254.3 1766.44,1254.3 1768.27,1254.31 \n",
       "  1770.09,1254.32 1771.92,1254.32 1773.75,1254.32 1775.57,1254.31 1777.4,1254.31 1779.23,1254.3 1781.05,1254.29 1782.88,1254.29 1784.71,1254.29 1786.53,1254.29 \n",
       "  1788.36,1254.3 1790.19,1254.31 1792.01,1254.31 1793.84,1254.32 1795.67,1254.32 1797.49,1254.31 1799.32,1254.31 1801.15,1254.3 1802.97,1254.29 1804.8,1254.29 \n",
       "  1806.62,1254.29 1808.45,1254.29 1810.28,1254.3 1812.1,1254.31 1813.93,1254.31 1815.76,1254.32 1817.58,1254.32 1819.41,1254.32 1821.24,1254.31 1823.06,1254.3 \n",
       "  1824.89,1254.3 1826.72,1254.29 1828.54,1254.29 1830.37,1254.29 1832.2,1254.29 1834.02,1254.3 1835.85,1254.31 1837.68,1254.31 1839.5,1254.32 1841.33,1254.32 \n",
       "  1843.16,1254.31 1844.98,1254.31 1846.81,1254.3 1848.64,1254.29 1850.46,1254.29 1852.29,1254.29 1854.11,1254.29 1855.94,1254.3 1857.77,1254.31 1859.59,1254.31 \n",
       "  1861.42,1254.32 1863.25,1254.32 1865.07,1254.32 1866.9,1254.31 1868.73,1254.3 1870.55,1254.3 1872.38,1254.29 1874.21,1254.29 1876.03,1254.29 1877.86,1254.29 \n",
       "  1879.69,1254.3 1881.51,1254.31 1883.34,1254.31 1885.17,1254.32 1886.99,1254.32 1888.82,1254.31 1890.65,1254.31 1892.47,1254.3 1894.3,1254.29 1896.12,1254.29 \n",
       "  1897.95,1254.29 1899.78,1254.29 1901.6,1254.3 1903.43,1254.31 1905.26,1254.31 1907.08,1254.32 1908.91,1254.32 1910.74,1254.32 1912.56,1254.31 1914.39,1254.3 \n",
       "  1916.22,1254.3 1918.04,1254.29 1919.87,1254.29 1921.7,1254.29 1923.52,1254.29 1925.35,1254.3 1927.18,1254.31 1929,1254.31 1930.83,1254.32 1932.66,1254.32 \n",
       "  1934.48,1254.31 1936.31,1254.31 1938.13,1254.3 1939.96,1254.29 1941.79,1254.29 1943.61,1254.29 1945.44,1254.29 1947.27,1254.3 1949.09,1254.31 1950.92,1254.31 \n",
       "  1952.75,1254.32 1954.57,1254.32 1956.4,1254.32 1958.23,1254.31 1960.05,1254.3 1961.88,1254.3 1963.71,1254.29 1965.53,1254.29 1967.36,1254.29 1969.19,1254.29 \n",
       "  1971.01,1254.3 1972.84,1254.31 1974.67,1254.31 1976.49,1254.32 1978.32,1254.32 1980.14,1254.31 1981.97,1254.31 1983.8,1254.3 1985.62,1254.29 1987.45,1254.29 \n",
       "  1989.28,1254.29 1991.1,1254.29 1992.93,1254.3 1994.76,1254.31 1996.58,1254.31 1998.41,1254.32 2000.24,1254.32 2002.06,1254.32 2003.89,1254.31 2005.72,1254.3 \n",
       "  2007.54,1254.3 2009.37,1254.29 2011.2,1254.29 2013.02,1254.29 2014.85,1254.3 2016.68,1254.3 2018.5,1254.31 2020.33,1254.31 2022.15,1254.32 2023.98,1254.32 \n",
       "  2025.81,1254.31 2027.63,1254.31 2029.46,1254.3 2031.29,1254.29 2033.11,1254.29 2034.94,1254.29 2036.77,1254.29 2038.59,1254.3 2040.42,1254.31 2042.25,1254.31 \n",
       "  2044.07,1254.32 2045.9,1254.32 2047.73,1254.32 2049.55,1254.31 2051.38,1254.3 2053.21,1254.3 2055.03,1254.29 2056.86,1254.29 2058.69,1254.29 2060.51,1254.3 \n",
       "  2062.34,1254.3 2064.16,1254.31 2065.99,1254.31 2067.82,1254.32 2069.64,1254.32 2071.47,1254.31 2073.3,1254.31 2075.12,1254.3 2076.95,1254.29 2078.78,1254.29 \n",
       "  2080.6,1254.29 2082.43,1254.29 2084.26,1254.3 2086.08,1254.31 2087.91,1254.31 2089.74,1254.32 2091.56,1254.32 2093.39,1254.32 2095.22,1254.31 2097.04,1254.3 \n",
       "  2098.87,1254.3 2100.7,1254.29 2102.52,1254.29 2104.35,1254.29 2106.18,1254.3 2108,1254.3 2109.83,1254.31 2111.65,1254.32 2113.48,1254.32 2115.31,1254.32 \n",
       "  2117.13,1254.31 2118.96,1254.31 2120.79,1254.3 2122.61,1254.29 2124.44,1254.29 2126.27,1254.29 2128.09,1254.29 2129.92,1254.3 2131.75,1254.31 2133.57,1254.31 \n",
       "  2135.4,1254.32 2137.23,1254.32 2139.05,1254.31 2140.88,1254.31 2142.71,1254.3 2144.53,1254.3 2146.36,1254.29 2148.19,1254.29 2150.01,1254.29 2151.84,1254.3 \n",
       "  2153.66,1254.3 2155.49,1254.31 2157.32,1254.32 2159.14,1254.32 2160.97,1254.32 2162.8,1254.31 2164.62,1254.31 2166.45,1254.3 2168.28,1254.29 2170.1,1254.29 \n",
       "  2171.93,1254.29 2173.76,1254.29 2175.58,1254.3 2177.41,1254.31 2179.24,1254.31 2181.06,1254.32 2182.89,1254.32 2184.72,1254.31 2186.54,1254.31 2188.37,1254.3 \n",
       "  2190.2,1254.3 2192.02,1254.29 2193.85,1254.29 2195.67,1254.29 2197.5,1254.3 2199.33,1254.3 2201.15,1254.31 2202.98,1254.32 2204.81,1254.32 2206.63,1254.32 \n",
       "  2208.46,1254.31 2210.29,1254.31 2212.11,1254.3 2213.94,1254.29 2215.77,1254.29 2217.59,1254.29 2219.42,1254.29 2221.25,1254.3 2223.07,1254.31 2224.9,1254.31 \n",
       "  2226.73,1254.32 2228.55,1254.32 2230.38,1254.31 2232.21,1254.31 2234.03,1254.3 2235.86,1254.29 2237.68,1254.29 2239.51,1254.29 2241.34,1254.29 2243.16,1254.3 \n",
       "  2244.99,1254.3 2246.82,1254.31 2248.64,1254.32 2250.47,1254.32 2252.3,1254.32 2254.12,1254.31 2255.95,1254.31 2257.78,1254.3 2259.6,1254.29 2261.43,1254.29 \n",
       "  2263.26,1254.29 2265.08,1254.29 2266.91,1254.3 2268.74,1254.31 2270.56,1254.31 2272.39,1254.32 2274.22,1254.32 2276.04,1254.31 2277.87,1254.31 2279.69,1254.3 \n",
       "  2281.52,1254.29 2283.35,1254.29 2285.17,1254.29 2287,1254.29 2288.83,1254.3 2290.65,1254.3 2292.48,1254.31 2294.31,1254.32 2296.13,1254.32 2297.96,1254.32 \n",
       "  2299.79,1254.31 2301.61,1254.31 2303.44,1254.3 2305.27,1254.29 2307.09,1254.29 2308.92,1254.29 2310.75,1254.29 2312.57,1254.3 2314.4,1254.31 2316.23,1254.31 \n",
       "  2318.05,1254.32 2319.88,1254.32 2321.7,1254.31 2323.53,1254.31 2325.36,1254.3 2327.18,1254.29 2329.01,1254.29 2330.84,1254.29 2332.66,1254.29 2334.49,1254.3 \n",
       "  2336.32,1254.3 2338.14,1254.31 2339.97,1254.31 2341.8,1254.31 2343.62,1254.31 2345.45,1254.31 2347.28,1254.3 2349.1,1254.3 2350.93,1254.29 2352.76,1254.29 \n",
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       "  509.792,1312.91 511.619,1312.88 513.445,1312.85 515.272,1312.83 517.099,1312.81 518.925,1312.8 520.752,1312.79 522.578,1312.79 524.405,1312.8 526.231,1312.81 \n",
       "  528.058,1312.82 529.884,1312.81 531.711,1312.79 533.537,1312.76 535.364,1312.73 537.19,1312.7 539.017,1312.68 540.843,1312.66 542.67,1312.65 544.496,1312.65 \n",
       "  546.323,1312.65 548.149,1312.66 549.976,1312.66 551.802,1312.66 553.629,1312.65 555.456,1312.63 557.282,1312.6 559.109,1312.58 560.935,1312.56 562.762,1312.54 \n",
       "  564.588,1312.54 566.415,1312.54 568.241,1312.54 570.068,1312.55 571.894,1312.57 573.721,1312.57 575.547,1312.57 577.374,1312.56 579.2,1312.54 581.027,1312.52 \n",
       "  582.853,1312.5 584.68,1312.49 586.506,1312.49 588.333,1312.49 590.159,1312.5 591.986,1312.51 593.813,1312.53 595.639,1312.55 597.466,1312.55 599.292,1312.55 \n",
       "  601.119,1312.54 602.945,1312.52 604.772,1312.5 606.598,1312.49 608.425,1312.49 610.251,1312.49 612.078,1312.5 613.904,1312.52 615.731,1312.54 617.557,1312.55 \n",
       "  619.384,1312.57 621.21,1312.57 623.037,1312.57 624.863,1312.55 626.69,1312.53 628.517,1312.52 630.343,1312.51 632.17,1312.51 633.996,1312.52 635.823,1312.53 \n",
       "  637.649,1312.55 639.476,1312.57 641.302,1312.58 643.129,1312.6 644.955,1312.59 646.782,1312.58 648.608,1312.56 650.435,1312.55 652.261,1312.53 654.088,1312.53 \n",
       "  655.914,1312.53 657.741,1312.54 659.567,1312.55 661.394,1312.57 663.22,1312.59 665.047,1312.6 666.874,1312.61 668.7,1312.6 670.527,1312.58 672.353,1312.56 \n",
       "  674.18,1312.55 676.006,1312.54 677.833,1312.53 679.659,1312.54 681.486,1312.55 683.312,1312.56 685.139,1312.58 686.965,1312.6 688.792,1312.61 690.618,1312.61 \n",
       "  692.445,1312.59 694.271,1312.57 696.098,1312.55 697.924,1312.54 699.751,1312.53 701.578,1312.53 703.404,1312.54 705.231,1312.55 707.057,1312.57 708.884,1312.59 \n",
       "  710.71,1312.6 712.537,1312.61 714.363,1312.59 716.19,1312.58 718.016,1312.56 719.843,1312.54 721.669,1312.53 723.496,1312.53 725.322,1312.53 727.149,1312.54 \n",
       "  728.975,1312.56 730.802,1312.58 732.628,1312.59 734.455,1312.6 736.281,1312.6 738.108,1312.58 739.935,1312.56 741.761,1312.55 743.588,1312.53 745.414,1312.53 \n",
       "  747.241,1312.53 749.067,1312.54 750.894,1312.55 752.72,1312.57 754.547,1312.59 756.373,1312.6 758.2,1312.6 760.026,1312.59 761.853,1312.57 763.679,1312.55 \n",
       "  765.506,1312.54 767.332,1312.53 769.159,1312.53 770.985,1312.53 772.812,1312.54 774.638,1312.56 776.465,1312.58 778.292,1312.59 780.118,1312.6 781.945,1312.6 \n",
       "  783.771,1312.58 785.598,1312.56 787.424,1312.55 789.251,1312.53 791.077,1312.53 792.904,1312.53 794.73,1312.54 796.557,1312.55 798.383,1312.57 800.21,1312.59 \n",
       "  802.036,1312.6 803.863,1312.6 805.689,1312.59 807.516,1312.57 809.342,1312.55 811.169,1312.54 812.996,1312.53 814.822,1312.53 816.649,1312.53 818.475,1312.54 \n",
       "  820.302,1312.56 822.128,1312.58 823.955,1312.59 825.781,1312.6 827.608,1312.6 829.434,1312.58 831.261,1312.56 833.087,1312.55 834.914,1312.53 836.74,1312.53 \n",
       "  838.567,1312.53 840.393,1312.54 842.22,1312.55 844.046,1312.57 845.873,1312.59 847.699,1312.6 849.526,1312.6 851.353,1312.59 853.179,1312.57 855.006,1312.55 \n",
       "  856.832,1312.54 858.659,1312.53 860.485,1312.53 862.312,1312.53 864.138,1312.54 865.965,1312.56 867.791,1312.58 869.618,1312.59 871.444,1312.6 873.271,1312.6 \n",
       "  875.097,1312.58 876.924,1312.56 878.75,1312.55 880.577,1312.53 882.403,1312.53 884.23,1312.53 886.057,1312.54 887.883,1312.55 889.71,1312.57 891.536,1312.59 \n",
       "  893.363,1312.6 895.189,1312.6 897.016,1312.59 898.842,1312.57 900.669,1312.55 902.495,1312.54 904.322,1312.53 906.148,1312.53 907.975,1312.53 909.801,1312.54 \n",
       "  911.628,1312.56 913.454,1312.58 915.281,1312.6 917.107,1312.6 918.934,1312.6 920.76,1312.58 922.587,1312.56 924.414,1312.54 926.24,1312.53 928.067,1312.53 \n",
       "  929.893,1312.53 931.72,1312.54 933.546,1312.55 935.373,1312.57 937.199,1312.59 939.026,1312.6 940.852,1312.6 942.679,1312.59 944.505,1312.57 946.332,1312.55 \n",
       "  948.158,1312.54 949.985,1312.53 951.811,1312.53 953.638,1312.53 955.464,1312.55 957.291,1312.56 959.117,1312.58 960.944,1312.6 962.771,1312.6 964.597,1312.6 \n",
       "  966.424,1312.58 968.25,1312.56 970.077,1312.54 971.903,1312.53 973.73,1312.53 975.556,1312.53 977.383,1312.54 979.209,1312.55 981.036,1312.57 982.862,1312.59 \n",
       "  984.689,1312.6 986.515,1312.6 988.342,1312.59 990.168,1312.57 991.995,1312.55 993.821,1312.54 995.648,1312.53 997.475,1312.53 999.301,1312.53 1001.13,1312.55 \n",
       "  1002.95,1312.56 1004.78,1312.58 1006.61,1312.6 1008.43,1312.6 1010.26,1312.59 1012.09,1312.58 1013.91,1312.56 1015.74,1312.54 1017.57,1312.53 1019.39,1312.53 \n",
       "  1021.22,1312.53 1023.05,1312.54 1024.87,1312.55 1026.7,1312.57 1028.53,1312.59 1030.35,1312.6 1032.18,1312.6 1034.01,1312.59 1035.83,1312.57 1037.66,1312.55 \n",
       "  1039.48,1312.54 1041.31,1312.53 1043.14,1312.53 1044.96,1312.53 1046.79,1312.55 1048.62,1312.56 1050.44,1312.58 1052.27,1312.6 1054.1,1312.6 1055.92,1312.59 \n",
       "  1057.75,1312.58 1059.58,1312.56 1061.4,1312.54 1063.23,1312.53 1065.06,1312.53 1066.88,1312.53 1068.71,1312.54 1070.54,1312.56 1072.36,1312.57 1074.19,1312.59 \n",
       "  1076.02,1312.6 1077.84,1312.6 1079.67,1312.59 1081.49,1312.57 1083.32,1312.55 1085.15,1312.54 1086.97,1312.53 1088.8,1312.53 1090.63,1312.53 1092.45,1312.55 \n",
       "  1094.28,1312.56 1096.11,1312.58 1097.93,1312.6 1099.76,1312.6 1101.59,1312.59 1103.41,1312.58 1105.24,1312.56 1107.07,1312.54 1108.89,1312.53 1110.72,1312.53 \n",
       "  1112.55,1312.53 1114.37,1312.54 1116.2,1312.56 1118.03,1312.57 1119.85,1312.59 1121.68,1312.6 1123.5,1312.6 1125.33,1312.59 1127.16,1312.57 1128.98,1312.55 \n",
       "  1130.81,1312.54 1132.64,1312.53 1134.46,1312.53 1136.29,1312.53 1138.12,1312.55 1139.94,1312.57 1141.77,1312.58 1143.6,1312.6 1145.42,1312.6 1147.25,1312.59 \n",
       "  1149.08,1312.58 1150.9,1312.56 1152.73,1312.54 1154.56,1312.53 1156.38,1312.53 1158.21,1312.53 1160.04,1312.54 1161.86,1312.56 1163.69,1312.57 1165.51,1312.59 \n",
       "  1167.34,1312.6 1169.17,1312.6 1170.99,1312.58 1172.82,1312.57 1174.65,1312.55 1176.47,1312.54 1178.3,1312.53 1180.13,1312.53 1181.95,1312.53 1183.78,1312.55 \n",
       "  1185.61,1312.57 1187.43,1312.58 1189.26,1312.6 1191.09,1312.6 1192.91,1312.59 1194.74,1312.58 1196.57,1312.56 1198.39,1312.54 1200.22,1312.53 1202.05,1312.53 \n",
       "  1203.87,1312.53 1205.7,1312.54 1207.52,1312.56 1209.35,1312.58 1211.18,1312.59 1213,1312.6 1214.83,1312.6 1216.66,1312.58 1218.48,1312.57 1220.31,1312.55 \n",
       "  1222.14,1312.53 1223.96,1312.53 1225.79,1312.53 1227.62,1312.54 1229.44,1312.55 1231.27,1312.57 1233.1,1312.58 1234.92,1312.6 1236.75,1312.6 1238.58,1312.59 \n",
       "  1240.4,1312.57 1242.23,1312.56 1244.06,1312.54 1245.88,1312.53 1247.71,1312.53 1249.53,1312.53 1251.36,1312.54 1253.19,1312.56 1255.01,1312.58 1256.84,1312.59 \n",
       "  1258.67,1312.6 1260.49,1312.6 1262.32,1312.58 1264.15,1312.57 1265.97,1312.55 1267.8,1312.53 1269.63,1312.53 1271.45,1312.53 1273.28,1312.54 1275.11,1312.55 \n",
       "  1276.93,1312.57 1278.76,1312.59 1280.59,1312.6 1282.41,1312.6 1284.24,1312.59 1286.07,1312.57 1287.89,1312.56 1289.72,1312.54 1291.55,1312.53 1293.37,1312.53 \n",
       "  1295.2,1312.53 1297.02,1312.54 1298.85,1312.56 1300.68,1312.58 1302.5,1312.59 1304.33,1312.6 1306.16,1312.6 1307.98,1312.58 1309.81,1312.56 1311.64,1312.55 \n",
       "  1313.46,1312.53 1315.29,1312.53 1317.12,1312.53 1318.94,1312.54 1320.77,1312.55 1322.6,1312.57 1324.42,1312.59 1326.25,1312.6 1328.08,1312.6 1329.9,1312.59 \n",
       "  1331.73,1312.57 1333.56,1312.56 1335.38,1312.54 1337.21,1312.53 1339.03,1312.53 1340.86,1312.53 1342.69,1312.54 1344.51,1312.56 1346.34,1312.58 1348.17,1312.59 \n",
       "  1349.99,1312.6 1351.82,1312.6 1353.65,1312.58 1355.47,1312.56 1357.3,1312.55 1359.13,1312.53 1360.95,1312.53 1362.78,1312.53 1364.61,1312.54 1366.43,1312.55 \n",
       "  1368.26,1312.57 1370.09,1312.59 1371.91,1312.6 1373.74,1312.6 1375.57,1312.59 1377.39,1312.57 1379.22,1312.55 1381.04,1312.54 1382.87,1312.53 1384.7,1312.53 \n",
       "  1386.52,1312.53 1388.35,1312.54 1390.18,1312.56 1392,1312.58 1393.83,1312.59 1395.66,1312.6 1397.48,1312.6 1399.31,1312.58 1401.14,1312.56 1402.96,1312.55 \n",
       "  1404.79,1312.53 1406.62,1312.53 1408.44,1312.53 1410.27,1312.54 1412.1,1312.55 1413.92,1312.57 1415.75,1312.59 1417.58,1312.6 1419.4,1312.6 1421.23,1312.59 \n",
       "  1423.05,1312.57 1424.88,1312.55 1426.71,1312.54 1428.53,1312.53 1430.36,1312.53 1432.19,1312.53 1434.01,1312.54 1435.84,1312.56 1437.67,1312.58 1439.49,1312.59 \n",
       "  1441.32,1312.6 1443.15,1312.6 1444.97,1312.58 1446.8,1312.56 1448.63,1312.55 1450.45,1312.53 1452.28,1312.53 1454.11,1312.53 1455.93,1312.54 1457.76,1312.55 \n",
       "  1459.59,1312.57 1461.41,1312.59 1463.24,1312.6 1465.06,1312.6 1466.89,1312.59 1468.72,1312.57 1470.54,1312.55 1472.37,1312.54 1474.2,1312.53 1476.02,1312.53 \n",
       "  1477.85,1312.53 1479.68,1312.54 1481.5,1312.56 1483.33,1312.58 1485.16,1312.6 1486.98,1312.6 1488.81,1312.6 1490.64,1312.58 1492.46,1312.56 1494.29,1312.54 \n",
       "  1496.12,1312.53 1497.94,1312.53 1499.77,1312.53 1501.6,1312.54 1503.42,1312.55 1505.25,1312.57 1507.07,1312.59 1508.9,1312.6 1510.73,1312.6 1512.55,1312.59 \n",
       "  1514.38,1312.57 1516.21,1312.55 1518.03,1312.54 1519.86,1312.53 1521.69,1312.53 1523.51,1312.53 1525.34,1312.55 1527.17,1312.56 1528.99,1312.58 1530.82,1312.6 \n",
       "  1532.65,1312.6 1534.47,1312.6 1536.3,1312.58 1538.13,1312.56 1539.95,1312.54 1541.78,1312.53 1543.61,1312.53 1545.43,1312.53 1547.26,1312.54 1549.09,1312.55 \n",
       "  1550.91,1312.57 1552.74,1312.59 1554.56,1312.6 1556.39,1312.6 1558.22,1312.59 1560.04,1312.57 1561.87,1312.55 1563.7,1312.54 1565.52,1312.53 1567.35,1312.53 \n",
       "  1569.18,1312.53 1571,1312.55 1572.83,1312.56 1574.66,1312.58 1576.48,1312.6 1578.31,1312.6 1580.14,1312.6 1581.96,1312.58 1583.79,1312.56 1585.62,1312.54 \n",
       "  1587.44,1312.53 1589.27,1312.53 1591.1,1312.53 1592.92,1312.54 1594.75,1312.55 1596.57,1312.57 1598.4,1312.59 1600.23,1312.6 1602.05,1312.6 1603.88,1312.59 \n",
       "  1605.71,1312.57 1607.53,1312.55 1609.36,1312.54 1611.19,1312.53 1613.01,1312.53 1614.84,1312.53 1616.67,1312.55 1618.49,1312.56 1620.32,1312.58 1622.15,1312.6 \n",
       "  1623.97,1312.6 1625.8,1312.59 1627.63,1312.58 1629.45,1312.56 1631.28,1312.54 1633.11,1312.53 1634.93,1312.53 1636.76,1312.53 1638.58,1312.54 1640.41,1312.55 \n",
       "  1642.24,1312.57 1644.06,1312.59 1645.89,1312.6 1647.72,1312.6 1649.54,1312.59 1651.37,1312.57 1653.2,1312.55 1655.02,1312.54 1656.85,1312.53 1658.68,1312.53 \n",
       "  1660.5,1312.53 1662.33,1312.55 1664.16,1312.56 1665.98,1312.58 1667.81,1312.6 1669.64,1312.6 1671.46,1312.59 1673.29,1312.58 1675.12,1312.56 1676.94,1312.54 \n",
       "  1678.77,1312.53 1680.59,1312.53 1682.42,1312.53 1684.25,1312.54 1686.07,1312.56 1687.9,1312.57 1689.73,1312.59 1691.55,1312.6 1693.38,1312.6 1695.21,1312.59 \n",
       "  1697.03,1312.57 1698.86,1312.55 1700.69,1312.54 1702.51,1312.53 1704.34,1312.53 1706.17,1312.53 1707.99,1312.55 1709.82,1312.56 1711.65,1312.58 1713.47,1312.6 \n",
       "  1715.3,1312.6 1717.13,1312.59 1718.95,1312.58 1720.78,1312.56 1722.6,1312.54 1724.43,1312.53 1726.26,1312.53 1728.08,1312.53 1729.91,1312.54 1731.74,1312.56 \n",
       "  1733.56,1312.57 1735.39,1312.59 1737.22,1312.6 1739.04,1312.6 1740.87,1312.59 1742.7,1312.57 1744.52,1312.55 1746.35,1312.54 1748.18,1312.53 1750,1312.53 \n",
       "  1751.83,1312.53 1753.66,1312.55 1755.48,1312.57 1757.31,1312.58 1759.14,1312.6 1760.96,1312.6 1762.79,1312.59 1764.61,1312.58 1766.44,1312.56 1768.27,1312.54 \n",
       "  1770.09,1312.53 1771.92,1312.53 1773.75,1312.53 1775.57,1312.54 1777.4,1312.56 1779.23,1312.57 1781.05,1312.59 1782.88,1312.6 1784.71,1312.6 1786.53,1312.58 \n",
       "  1788.36,1312.57 1790.19,1312.55 1792.01,1312.54 1793.84,1312.53 1795.67,1312.53 1797.49,1312.54 1799.32,1312.55 1801.15,1312.57 1802.97,1312.58 1804.8,1312.6 \n",
       "  1806.62,1312.6 1808.45,1312.59 1810.28,1312.58 1812.1,1312.56 1813.93,1312.54 1815.76,1312.53 1817.58,1312.53 1819.41,1312.53 1821.24,1312.54 1823.06,1312.56 \n",
       "  1824.89,1312.58 1826.72,1312.59 1828.54,1312.6 1830.37,1312.6 1832.2,1312.58 1834.02,1312.57 1835.85,1312.55 1837.68,1312.53 1839.5,1312.53 1841.33,1312.53 \n",
       "  1843.16,1312.54 1844.98,1312.55 1846.81,1312.57 1848.64,1312.58 1850.46,1312.6 1852.29,1312.6 1854.11,1312.59 1855.94,1312.57 1857.77,1312.56 1859.59,1312.54 \n",
       "  1861.42,1312.53 1863.25,1312.53 1865.07,1312.53 1866.9,1312.54 1868.73,1312.56 1870.55,1312.58 1872.38,1312.59 1874.21,1312.6 1876.03,1312.6 1877.86,1312.58 \n",
       "  1879.69,1312.56 1881.51,1312.55 1883.34,1312.53 1885.17,1312.53 1886.99,1312.53 1888.82,1312.54 1890.65,1312.55 1892.47,1312.57 1894.3,1312.59 1896.12,1312.6 \n",
       "  1897.95,1312.6 1899.78,1312.59 1901.6,1312.57 1903.43,1312.56 1905.26,1312.54 1907.08,1312.53 1908.91,1312.53 1910.74,1312.53 1912.56,1312.54 1914.39,1312.56 \n",
       "  1916.22,1312.58 1918.04,1312.59 1919.87,1312.6 1921.7,1312.6 1923.52,1312.58 1925.35,1312.56 1927.18,1312.55 1929,1312.53 1930.83,1312.53 1932.66,1312.53 \n",
       "  1934.48,1312.54 1936.31,1312.55 1938.13,1312.57 1939.96,1312.59 1941.79,1312.6 1943.61,1312.6 1945.44,1312.59 1947.27,1312.57 1949.09,1312.55 1950.92,1312.54 \n",
       "  1952.75,1312.53 1954.57,1312.53 1956.4,1312.53 1958.23,1312.54 1960.05,1312.56 1961.88,1312.58 1963.71,1312.59 1965.53,1312.6 1967.36,1312.6 1969.19,1312.58 \n",
       "  1971.01,1312.56 1972.84,1312.55 1974.67,1312.53 1976.49,1312.53 1978.32,1312.53 1980.14,1312.54 1981.97,1312.55 1983.8,1312.57 1985.62,1312.59 1987.45,1312.6 \n",
       "  1989.28,1312.6 1991.1,1312.59 1992.93,1312.57 1994.76,1312.55 1996.58,1312.54 1998.41,1312.53 2000.24,1312.53 2002.06,1312.53 2003.89,1312.54 2005.72,1312.56 \n",
       "  2007.54,1312.58 2009.37,1312.59 2011.2,1312.6 2013.02,1312.6 2014.85,1312.58 2016.68,1312.56 2018.5,1312.55 2020.33,1312.53 2022.15,1312.53 2023.98,1312.53 \n",
       "  2025.81,1312.54 2027.63,1312.55 2029.46,1312.57 2031.29,1312.59 2033.11,1312.6 2034.94,1312.6 2036.77,1312.59 2038.59,1312.57 2040.42,1312.55 2042.25,1312.54 \n",
       "  2044.07,1312.53 2045.9,1312.53 2047.73,1312.53 2049.55,1312.54 2051.38,1312.56 2053.21,1312.58 2055.03,1312.59 2056.86,1312.6 2058.69,1312.6 2060.51,1312.58 \n",
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       "  1404.79,1382.94 1406.62,1382.94 1408.44,1382.94 1410.27,1382.94 1412.1,1382.94 1413.92,1382.94 1415.75,1382.94 1417.58,1382.94 1419.4,1382.94 1421.23,1382.94 \n",
       "  1423.05,1382.94 1424.88,1382.94 1426.71,1382.94 1428.53,1382.94 1430.36,1382.94 1432.19,1382.94 1434.01,1382.94 1435.84,1382.94 1437.67,1382.94 1439.49,1382.94 \n",
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       "  1697.03,1382.94 1698.86,1382.94 1700.69,1382.94 1702.51,1382.94 1704.34,1382.94 1706.17,1382.94 1707.99,1382.94 1709.82,1382.94 1711.65,1382.94 1713.47,1382.94 \n",
       "  1715.3,1382.94 1717.13,1382.94 1718.95,1382.94 1720.78,1382.94 1722.6,1382.94 1724.43,1382.94 1726.26,1382.94 1728.08,1382.94 1729.91,1382.94 1731.74,1382.94 \n",
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       "  1788.36,1382.94 1790.19,1382.94 1792.01,1382.94 1793.84,1382.94 1795.67,1382.94 1797.49,1382.94 1799.32,1382.94 1801.15,1382.94 1802.97,1382.94 1804.8,1382.94 \n",
       "  1806.62,1382.94 1808.45,1382.94 1810.28,1382.94 1812.1,1382.94 1813.93,1382.94 1815.76,1382.94 1817.58,1382.94 1819.41,1382.94 1821.24,1382.94 1823.06,1382.94 \n",
       "  1824.89,1382.94 1826.72,1382.94 1828.54,1382.94 1830.37,1382.94 1832.2,1382.94 1834.02,1382.94 1835.85,1382.94 1837.68,1382.94 1839.5,1382.94 1841.33,1382.94 \n",
       "  1843.16,1382.94 1844.98,1382.94 1846.81,1382.94 1848.64,1382.94 1850.46,1382.94 1852.29,1382.94 1854.11,1382.94 1855.94,1382.94 1857.77,1382.94 1859.59,1382.94 \n",
       "  1861.42,1382.94 1863.25,1382.94 1865.07,1382.94 1866.9,1382.94 1868.73,1382.94 1870.55,1382.94 1872.38,1382.94 1874.21,1382.94 1876.03,1382.94 1877.86,1382.94 \n",
       "  1879.69,1382.94 1881.51,1382.94 1883.34,1382.94 1885.17,1382.94 1886.99,1382.94 1888.82,1382.94 1890.65,1382.94 1892.47,1382.94 1894.3,1382.94 1896.12,1382.94 \n",
       "  1897.95,1382.94 1899.78,1382.94 1901.6,1382.94 1903.43,1382.94 1905.26,1382.94 1907.08,1382.94 1908.91,1382.94 1910.74,1382.94 1912.56,1382.94 1914.39,1382.94 \n",
       "  1916.22,1382.94 1918.04,1382.94 1919.87,1382.94 1921.7,1382.94 1923.52,1382.94 1925.35,1382.94 1927.18,1382.94 1929,1382.94 1930.83,1382.94 1932.66,1382.94 \n",
       "  1934.48,1382.94 1936.31,1382.94 1938.13,1382.94 1939.96,1382.94 1941.79,1382.94 1943.61,1382.94 1945.44,1382.94 1947.27,1382.94 1949.09,1382.94 1950.92,1382.94 \n",
       "  1952.75,1382.94 1954.57,1382.94 1956.4,1382.94 1958.23,1382.94 1960.05,1382.94 1961.88,1382.94 1963.71,1382.94 1965.53,1382.94 1967.36,1382.94 1969.19,1382.94 \n",
       "  1971.01,1382.94 1972.84,1382.94 1974.67,1382.94 1976.49,1382.94 1978.32,1382.94 1980.14,1382.94 1981.97,1382.94 1983.8,1382.94 1985.62,1382.94 1987.45,1382.94 \n",
       "  1989.28,1382.94 1991.1,1382.94 1992.93,1382.94 1994.76,1382.94 1996.58,1382.94 1998.41,1382.94 2000.24,1382.94 2002.06,1382.94 2003.89,1382.94 2005.72,1382.94 \n",
       "  2007.54,1382.94 2009.37,1382.94 2011.2,1382.94 2013.02,1382.94 2014.85,1382.94 2016.68,1382.94 2018.5,1382.94 2020.33,1382.94 2022.15,1382.94 2023.98,1382.94 \n",
       "  2025.81,1382.94 2027.63,1382.94 2029.46,1382.94 2031.29,1382.94 2033.11,1382.94 2034.94,1382.94 2036.77,1382.94 2038.59,1382.94 2040.42,1382.94 2042.25,1382.94 \n",
       "  2044.07,1382.94 2045.9,1382.94 2047.73,1382.94 2049.55,1382.94 2051.38,1382.94 2053.21,1382.94 2055.03,1382.94 2056.86,1382.94 2058.69,1382.94 2060.51,1382.94 \n",
       "  2062.34,1382.94 2064.16,1382.94 2065.99,1382.94 2067.82,1382.94 2069.64,1382.94 2071.47,1382.94 2073.3,1382.94 2075.12,1382.94 2076.95,1382.94 2078.78,1382.94 \n",
       "  2080.6,1382.94 2082.43,1382.94 2084.26,1382.94 2086.08,1382.94 2087.91,1382.94 2089.74,1382.94 2091.56,1382.94 2093.39,1382.94 2095.22,1382.94 2097.04,1382.94 \n",
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       "  2117.13,1382.94 2118.96,1382.94 2120.79,1382.94 2122.61,1382.94 2124.44,1382.94 2126.27,1382.94 2128.09,1382.94 2129.92,1382.94 2131.75,1382.94 2133.57,1382.94 \n",
       "  2135.4,1382.94 2137.23,1382.94 2139.05,1382.94 2140.88,1382.94 2142.71,1382.94 2144.53,1382.94 2146.36,1382.94 2148.19,1382.94 2150.01,1382.94 2151.84,1382.94 \n",
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       "  2336.32,1382.94 2338.14,1382.94 2339.97,1382.94 2341.8,1382.94 2343.62,1382.94 2345.45,1382.94 2347.28,1382.94 2349.1,1382.94 2350.93,1382.94 2352.76,1382.94 \n",
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       "  728.975,1240.89 730.802,1240.88 732.628,1240.86 734.455,1240.86 736.281,1240.86 738.108,1240.87 739.935,1240.89 741.761,1240.9 743.588,1240.91 745.414,1240.92 \n",
       "  747.241,1240.92 749.067,1240.91 750.894,1240.9 752.72,1240.88 754.547,1240.87 756.373,1240.85 758.2,1240.85 760.026,1240.86 761.853,1240.88 763.679,1240.89 \n",
       "  765.506,1240.9 767.332,1240.91 769.159,1240.92 770.985,1240.91 772.812,1240.9 774.638,1240.89 776.465,1240.87 778.292,1240.86 780.118,1240.85 781.945,1240.85 \n",
       "  783.771,1240.87 785.598,1240.88 787.424,1240.9 789.251,1240.91 791.077,1240.91 792.904,1240.91 794.73,1240.91 796.557,1240.89 798.383,1240.88 800.21,1240.86 \n",
       "  802.036,1240.85 803.863,1240.85 805.689,1240.86 807.516,1240.88 809.342,1240.89 811.169,1240.9 812.996,1240.91 814.822,1240.91 816.649,1240.91 818.475,1240.9 \n",
       "  820.302,1240.89 822.128,1240.87 823.955,1240.86 825.781,1240.85 827.608,1240.85 829.434,1240.87 831.261,1240.88 833.087,1240.9 834.914,1240.91 836.74,1240.91 \n",
       "  838.567,1240.91 840.393,1240.91 842.22,1240.89 844.046,1240.88 845.873,1240.86 847.699,1240.85 849.526,1240.85 851.353,1240.86 853.179,1240.88 855.006,1240.89 \n",
       "  856.832,1240.91 858.659,1240.91 860.485,1240.92 862.312,1240.91 864.138,1240.9 865.965,1240.89 867.791,1240.87 869.618,1240.86 871.444,1240.85 873.271,1240.86 \n",
       "  875.097,1240.87 876.924,1240.89 878.75,1240.9 880.577,1240.91 882.403,1240.92 884.23,1240.91 886.057,1240.91 887.883,1240.89 889.71,1240.88 891.536,1240.86 \n",
       "  893.363,1240.85 895.189,1240.85 897.016,1240.86 898.842,1240.88 900.669,1240.89 902.495,1240.91 904.322,1240.91 906.148,1240.92 907.975,1240.91 909.801,1240.9 \n",
       "  911.628,1240.89 913.454,1240.87 915.281,1240.86 917.107,1240.85 918.934,1240.86 920.76,1240.87 922.587,1240.89 924.414,1240.9 926.24,1240.91 928.067,1240.92 \n",
       "  929.893,1240.91 931.72,1240.91 933.546,1240.89 935.373,1240.88 937.199,1240.86 939.026,1240.85 940.852,1240.85 942.679,1240.86 944.505,1240.88 946.332,1240.89 \n",
       "  948.158,1240.91 949.985,1240.91 951.811,1240.92 953.638,1240.91 955.464,1240.9 957.291,1240.88 959.117,1240.87 960.944,1240.86 962.771,1240.85 964.597,1240.86 \n",
       "  966.424,1240.87 968.25,1240.89 970.077,1240.9 971.903,1240.91 973.73,1240.92 975.556,1240.91 977.383,1240.91 979.209,1240.89 981.036,1240.88 982.862,1240.86 \n",
       "  984.689,1240.85 986.515,1240.85 988.342,1240.86 990.168,1240.88 991.995,1240.89 993.821,1240.91 995.648,1240.91 997.475,1240.92 999.301,1240.91 1001.13,1240.9 \n",
       "  1002.95,1240.88 1004.78,1240.87 1006.61,1240.86 1008.43,1240.85 1010.26,1240.86 1012.09,1240.87 1013.91,1240.89 1015.74,1240.9 1017.57,1240.91 1019.39,1240.92 \n",
       "  1021.22,1240.91 1023.05,1240.9 1024.87,1240.89 1026.7,1240.88 1028.53,1240.86 1030.35,1240.85 1032.18,1240.85 1034.01,1240.86 1035.83,1240.88 1037.66,1240.89 \n",
       "  1039.48,1240.91 1041.31,1240.91 1043.14,1240.92 1044.96,1240.91 1046.79,1240.9 1048.62,1240.88 1050.44,1240.87 1052.27,1240.86 1054.1,1240.85 1055.92,1240.86 \n",
       "  1057.75,1240.87 1059.58,1240.89 1061.4,1240.9 1063.23,1240.91 1065.06,1240.92 1066.88,1240.91 1068.71,1240.9 1070.54,1240.89 1072.36,1240.88 1074.19,1240.86 \n",
       "  1076.02,1240.85 1077.84,1240.85 1079.67,1240.86 1081.49,1240.88 1083.32,1240.9 1085.15,1240.91 1086.97,1240.91 1088.8,1240.91 1090.63,1240.91 1092.45,1240.9 \n",
       "  1094.28,1240.88 1096.11,1240.87 1097.93,1240.85 1099.76,1240.85 1101.59,1240.86 1103.41,1240.87 1105.24,1240.89 1107.07,1240.9 1108.89,1240.91 1110.72,1240.92 \n",
       "  1112.55,1240.91 1114.37,1240.9 1116.2,1240.89 1118.03,1240.87 1119.85,1240.86 1121.68,1240.85 1123.5,1240.85 1125.33,1240.86 1127.16,1240.88 1128.98,1240.9 \n",
       "  1130.81,1240.91 1132.64,1240.91 1134.46,1240.91 1136.29,1240.91 1138.12,1240.9 1139.94,1240.88 1141.77,1240.87 1143.6,1240.85 1145.42,1240.85 1147.25,1240.86 \n",
       "  1149.08,1240.87 1150.9,1240.89 1152.73,1240.9 1154.56,1240.91 1156.38,1240.92 1158.21,1240.91 1160.04,1240.9 1161.86,1240.89 1163.69,1240.87 1165.51,1240.86 \n",
       "  1167.34,1240.85 1169.17,1240.85 1170.99,1240.87 1172.82,1240.88 1174.65,1240.9 1176.47,1240.91 1178.3,1240.91 1180.13,1240.91 1181.95,1240.91 1183.78,1240.9 \n",
       "  1185.61,1240.88 1187.43,1240.87 1189.26,1240.85 1191.09,1240.85 1192.91,1240.86 1194.74,1240.87 1196.57,1240.89 1198.39,1240.9 1200.22,1240.91 1202.05,1240.92 \n",
       "  1203.87,1240.91 1205.7,1240.9 1207.52,1240.89 1209.35,1240.87 1211.18,1240.86 1213,1240.85 1214.83,1240.85 1216.66,1240.87 1218.48,1240.88 1220.31,1240.9 \n",
       "  1222.14,1240.91 1223.96,1240.91 1225.79,1240.91 1227.62,1240.91 1229.44,1240.9 1231.27,1240.88 1233.1,1240.87 1234.92,1240.85 1236.75,1240.85 1238.58,1240.86 \n",
       "  1240.4,1240.87 1242.23,1240.89 1244.06,1240.9 1245.88,1240.91 1247.71,1240.92 1249.53,1240.91 1251.36,1240.9 1253.19,1240.89 1255.01,1240.87 1256.84,1240.86 \n",
       "  1258.67,1240.85 1260.49,1240.85 1262.32,1240.87 1264.15,1240.88 1265.97,1240.9 1267.8,1240.91 1269.63,1240.91 1271.45,1240.91 1273.28,1240.91 1275.11,1240.9 \n",
       "  1276.93,1240.88 1278.76,1240.87 1280.59,1240.85 1282.41,1240.85 1284.24,1240.86 1286.07,1240.87 1287.89,1240.89 1289.72,1240.9 1291.55,1240.91 1293.37,1240.92 \n",
       "  1295.2,1240.91 1297.02,1240.9 1298.85,1240.89 1300.68,1240.87 1302.5,1240.86 1304.33,1240.85 1306.16,1240.85 1307.98,1240.87 1309.81,1240.88 1311.64,1240.9 \n",
       "  1313.46,1240.91 1315.29,1240.92 1317.12,1240.91 1318.94,1240.91 1320.77,1240.9 1322.6,1240.88 1324.42,1240.86 1326.25,1240.85 1328.08,1240.85 1329.9,1240.86 \n",
       "  1331.73,1240.88 1333.56,1240.89 1335.38,1240.9 1337.21,1240.91 1339.03,1240.92 1340.86,1240.91 1342.69,1240.9 1344.51,1240.89 1346.34,1240.87 1348.17,1240.86 \n",
       "  1349.99,1240.85 1351.82,1240.85 1353.65,1240.87 1355.47,1240.88 1357.3,1240.9 1359.13,1240.91 1360.95,1240.92 1362.78,1240.91 1364.61,1240.91 1366.43,1240.89 \n",
       "  1368.26,1240.88 1370.09,1240.86 1371.91,1240.85 1373.74,1240.85 1375.57,1240.86 1377.39,1240.88 1379.22,1240.89 1381.04,1240.9 1382.87,1240.91 1384.7,1240.92 \n",
       "  1386.52,1240.91 1388.35,1240.9 1390.18,1240.89 1392,1240.87 1393.83,1240.86 1395.66,1240.85 1397.48,1240.85 1399.31,1240.87 1401.14,1240.88 1402.96,1240.9 \n",
       "  1404.79,1240.91 1406.62,1240.92 1408.44,1240.91 1410.27,1240.91 1412.1,1240.89 1413.92,1240.88 1415.75,1240.86 1417.58,1240.85 1419.4,1240.85 1421.23,1240.86 \n",
       "  1423.05,1240.88 1424.88,1240.89 1426.71,1240.91 1428.53,1240.91 1430.36,1240.92 1432.19,1240.91 1434.01,1240.9 1435.84,1240.89 1437.67,1240.87 1439.49,1240.86 \n",
       "  1441.32,1240.85 1443.15,1240.86 1444.97,1240.87 1446.8,1240.88 1448.63,1240.9 1450.45,1240.91 1452.28,1240.92 1454.11,1240.91 1455.93,1240.91 1457.76,1240.89 \n",
       "  1459.59,1240.88 1461.41,1240.86 1463.24,1240.85 1465.06,1240.85 1466.89,1240.86 1468.72,1240.88 1470.54,1240.89 1472.37,1240.91 1474.2,1240.91 1476.02,1240.92 \n",
       "  1477.85,1240.91 1479.68,1240.9 1481.5,1240.89 1483.33,1240.87 1485.16,1240.86 1486.98,1240.85 1488.81,1240.86 1490.64,1240.87 1492.46,1240.89 1494.29,1240.9 \n",
       "  1496.12,1240.91 1497.94,1240.92 1499.77,1240.91 1501.6,1240.91 1503.42,1240.89 1505.25,1240.88 1507.07,1240.86 1508.9,1240.85 1510.73,1240.85 1512.55,1240.86 \n",
       "  1514.38,1240.88 1516.21,1240.89 1518.03,1240.91 1519.86,1240.91 1521.69,1240.92 1523.51,1240.91 1525.34,1240.9 1527.17,1240.89 1528.99,1240.87 1530.82,1240.86 \n",
       "  1532.65,1240.85 1534.47,1240.86 1536.3,1240.87 1538.13,1240.89 1539.95,1240.9 1541.78,1240.91 1543.61,1240.92 1545.43,1240.91 1547.26,1240.91 1549.09,1240.89 \n",
       "  1550.91,1240.88 1552.74,1240.86 1554.56,1240.85 1556.39,1240.85 1558.22,1240.86 1560.04,1240.88 1561.87,1240.89 1563.7,1240.91 1565.52,1240.91 1567.35,1240.92 \n",
       "  1569.18,1240.91 1571,1240.9 1572.83,1240.88 1574.66,1240.87 1576.48,1240.86 1578.31,1240.85 1580.14,1240.86 1581.96,1240.87 1583.79,1240.89 1585.62,1240.9 \n",
       "  1587.44,1240.91 1589.27,1240.92 1591.1,1240.91 1592.92,1240.91 1594.75,1240.89 1596.57,1240.88 1598.4,1240.86 1600.23,1240.85 1602.05,1240.85 1603.88,1240.86 \n",
       "  1605.71,1240.88 1607.53,1240.89 1609.36,1240.91 1611.19,1240.91 1613.01,1240.92 1614.84,1240.91 1616.67,1240.9 1618.49,1240.88 1620.32,1240.87 1622.15,1240.86 \n",
       "  1623.97,1240.85 1625.8,1240.86 1627.63,1240.87 1629.45,1240.89 1631.28,1240.9 1633.11,1240.91 1634.93,1240.92 1636.76,1240.91 1638.58,1240.9 1640.41,1240.89 \n",
       "  1642.24,1240.88 1644.06,1240.86 1645.89,1240.85 1647.72,1240.85 1649.54,1240.86 1651.37,1240.88 1653.2,1240.89 1655.02,1240.91 1656.85,1240.91 1658.68,1240.92 \n",
       "  1660.5,1240.91 1662.33,1240.9 1664.16,1240.88 1665.98,1240.87 1667.81,1240.85 1669.64,1240.85 1671.46,1240.86 1673.29,1240.87 1675.12,1240.89 1676.94,1240.9 \n",
       "  1678.77,1240.91 1680.59,1240.92 1682.42,1240.91 1684.25,1240.9 1686.07,1240.89 1687.9,1240.88 1689.73,1240.86 1691.55,1240.85 1693.38,1240.85 1695.21,1240.86 \n",
       "  1697.03,1240.88 1698.86,1240.9 1700.69,1240.91 1702.51,1240.91 1704.34,1240.91 1706.17,1240.91 1707.99,1240.9 1709.82,1240.88 1711.65,1240.87 1713.47,1240.85 \n",
       "  1715.3,1240.85 1717.13,1240.86 1718.95,1240.87 1720.78,1240.89 1722.6,1240.9 1724.43,1240.91 1726.26,1240.92 1728.08,1240.91 1729.91,1240.9 1731.74,1240.89 \n",
       "  1733.56,1240.87 1735.39,1240.86 1737.22,1240.85 1739.04,1240.85 1740.87,1240.86 1742.7,1240.88 1744.52,1240.9 1746.35,1240.91 1748.18,1240.91 1750,1240.91 \n",
       "  1751.83,1240.91 1753.66,1240.9 1755.48,1240.88 1757.31,1240.87 1759.14,1240.85 1760.96,1240.85 1762.79,1240.86 1764.61,1240.87 1766.44,1240.89 1768.27,1240.9 \n",
       "  1770.09,1240.91 1771.92,1240.92 1773.75,1240.91 1775.57,1240.9 1777.4,1240.89 1779.23,1240.87 1781.05,1240.86 1782.88,1240.85 1784.71,1240.85 1786.53,1240.87 \n",
       "  1788.36,1240.88 1790.19,1240.9 1792.01,1240.91 1793.84,1240.91 1795.67,1240.91 1797.49,1240.91 1799.32,1240.9 1801.15,1240.88 1802.97,1240.87 1804.8,1240.85 \n",
       "  1806.62,1240.85 1808.45,1240.86 1810.28,1240.87 1812.1,1240.89 1813.93,1240.9 1815.76,1240.91 1817.58,1240.92 1819.41,1240.91 1821.24,1240.9 1823.06,1240.89 \n",
       "  1824.89,1240.87 1826.72,1240.86 1828.54,1240.85 1830.37,1240.85 1832.2,1240.87 1834.02,1240.88 1835.85,1240.9 1837.68,1240.91 1839.5,1240.91 1841.33,1240.91 \n",
       "  1843.16,1240.91 1844.98,1240.9 1846.81,1240.88 1848.64,1240.87 1850.46,1240.85 1852.29,1240.85 1854.11,1240.86 1855.94,1240.87 1857.77,1240.89 1859.59,1240.9 \n",
       "  1861.42,1240.91 1863.25,1240.92 1865.07,1240.91 1866.9,1240.9 1868.73,1240.89 1870.55,1240.87 1872.38,1240.86 1874.21,1240.85 1876.03,1240.85 1877.86,1240.87 \n",
       "  1879.69,1240.88 1881.51,1240.9 1883.34,1240.91 1885.17,1240.91 1886.99,1240.91 1888.82,1240.91 1890.65,1240.9 1892.47,1240.88 1894.3,1240.86 1896.12,1240.85 \n",
       "  1897.95,1240.85 1899.78,1240.86 1901.6,1240.87 1903.43,1240.89 1905.26,1240.9 1907.08,1240.91 1908.91,1240.92 1910.74,1240.91 1912.56,1240.9 1914.39,1240.89 \n",
       "  1916.22,1240.87 1918.04,1240.86 1919.87,1240.85 1921.7,1240.85 1923.52,1240.87 1925.35,1240.88 1927.18,1240.9 1929,1240.91 1930.83,1240.92 1932.66,1240.91 \n",
       "  1934.48,1240.91 1936.31,1240.9 1938.13,1240.88 1939.96,1240.86 1941.79,1240.85 1943.61,1240.85 1945.44,1240.86 1947.27,1240.88 1949.09,1240.89 1950.92,1240.9 \n",
       "  1952.75,1240.91 1954.57,1240.92 1956.4,1240.91 1958.23,1240.9 1960.05,1240.89 1961.88,1240.87 1963.71,1240.86 1965.53,1240.85 1967.36,1240.85 1969.19,1240.87 \n",
       "  1971.01,1240.88 1972.84,1240.9 1974.67,1240.91 1976.49,1240.92 1978.32,1240.91 1980.14,1240.91 1981.97,1240.89 1983.8,1240.88 1985.62,1240.86 1987.45,1240.85 \n",
       "  1989.28,1240.85 1991.1,1240.86 1992.93,1240.88 1994.76,1240.89 1996.58,1240.91 1998.41,1240.91 2000.24,1240.92 2002.06,1240.91 2003.89,1240.9 2005.72,1240.89 \n",
       "  2007.54,1240.87 2009.37,1240.86 2011.2,1240.85 2013.02,1240.85 2014.85,1240.87 2016.68,1240.88 2018.5,1240.9 2020.33,1240.91 2022.15,1240.92 2023.98,1240.91 \n",
       "  2025.81,1240.91 2027.63,1240.89 2029.46,1240.88 2031.29,1240.86 2033.11,1240.85 2034.94,1240.85 2036.77,1240.86 2038.59,1240.88 2040.42,1240.89 2042.25,1240.91 \n",
       "  2044.07,1240.91 2045.9,1240.92 2047.73,1240.91 2049.55,1240.9 2051.38,1240.89 2053.21,1240.87 2055.03,1240.86 2056.86,1240.85 2058.69,1240.86 2060.51,1240.87 \n",
       "  2062.34,1240.88 2064.16,1240.9 2065.99,1240.91 2067.82,1240.92 2069.64,1240.91 2071.47,1240.91 2073.3,1240.89 2075.12,1240.88 2076.95,1240.86 2078.78,1240.85 \n",
       "  2080.6,1240.85 2082.43,1240.86 2084.26,1240.88 2086.08,1240.89 2087.91,1240.91 2089.74,1240.91 2091.56,1240.92 2093.39,1240.91 2095.22,1240.9 2097.04,1240.89 \n",
       "  2098.87,1240.87 2100.7,1240.86 2102.52,1240.85 2104.35,1240.86 2106.18,1240.87 2108,1240.89 2109.83,1240.9 2111.65,1240.91 2113.48,1240.92 2115.31,1240.91 \n",
       "  2117.13,1240.91 2118.96,1240.89 2120.79,1240.88 2122.61,1240.86 2124.44,1240.85 2126.27,1240.85 2128.09,1240.86 2129.92,1240.88 2131.75,1240.89 2133.57,1240.91 \n",
       "  2135.4,1240.91 2137.23,1240.92 2139.05,1240.91 2140.88,1240.9 2142.71,1240.88 2144.53,1240.87 2146.36,1240.86 2148.19,1240.85 2150.01,1240.86 2151.84,1240.87 \n",
       "  2153.66,1240.89 2155.49,1240.9 2157.32,1240.91 2159.14,1240.92 2160.97,1240.91 2162.8,1240.91 2164.62,1240.89 2166.45,1240.88 2168.28,1240.86 2170.1,1240.85 \n",
       "  2171.93,1240.85 2173.76,1240.86 2175.58,1240.88 2177.41,1240.89 2179.24,1240.91 2181.06,1240.91 2182.89,1240.92 2184.72,1240.91 2186.54,1240.9 2188.37,1240.88 \n",
       "  2190.2,1240.87 2192.02,1240.86 2193.85,1240.85 2195.67,1240.86 2197.5,1240.87 2199.33,1240.89 2201.15,1240.9 2202.98,1240.91 2204.81,1240.92 2206.63,1240.91 \n",
       "  2208.46,1240.9 2210.29,1240.89 2212.11,1240.88 2213.94,1240.86 2215.77,1240.85 2217.59,1240.85 2219.42,1240.86 2221.25,1240.88 2223.07,1240.89 2224.9,1240.91 \n",
       "  2226.73,1240.91 2228.55,1240.92 2230.38,1240.91 2232.21,1240.9 2234.03,1240.88 2235.86,1240.87 2237.68,1240.86 2239.51,1240.85 2241.34,1240.86 2243.16,1240.87 \n",
       "  2244.99,1240.89 2246.82,1240.9 2248.64,1240.91 2250.47,1240.92 2252.3,1240.91 2254.12,1240.9 2255.95,1240.89 2257.78,1240.88 2259.6,1240.86 2261.43,1240.85 \n",
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       "  1733.56,428.555 1735.39,428.56 1737.22,428.563 1739.04,428.562 1740.87,428.558 1742.7,428.553 1744.52,428.548 1746.35,428.544 1748.18,428.542 1750,428.542 \n",
       "  1751.83,428.544 1753.66,428.548 1755.48,428.553 1757.31,428.558 1759.14,428.561 1760.96,428.563 1762.79,428.56 1764.61,428.555 1766.44,428.55 1768.27,428.546 \n",
       "  1770.09,428.543 1771.92,428.542 1773.75,428.543 1775.57,428.546 1777.4,428.55 1779.23,428.555 1781.05,428.56 1782.88,428.563 1784.71,428.562 1786.53,428.558 \n",
       "  1788.36,428.553 1790.19,428.548 1792.01,428.544 1793.84,428.542 1795.67,428.542 1797.49,428.544 1799.32,428.548 1801.15,428.553 1802.97,428.558 1804.8,428.562 \n",
       "  1806.62,428.563 1808.45,428.56 1810.28,428.555 1812.1,428.55 1813.93,428.546 1815.76,428.543 1817.58,428.542 1819.41,428.543 1821.24,428.546 1823.06,428.55 \n",
       "  1824.89,428.555 1826.72,428.56 1828.54,428.563 1830.37,428.562 1832.2,428.558 1834.02,428.553 1835.85,428.548 1837.68,428.544 1839.5,428.542 1841.33,428.542 \n",
       "  1843.16,428.544 1844.98,428.548 1846.81,428.553 1848.64,428.558 1850.46,428.562 1852.29,428.563 1854.11,428.56 1855.94,428.555 1857.77,428.55 1859.59,428.546 \n",
       "  1861.42,428.543 1863.25,428.542 1865.07,428.543 1866.9,428.546 1868.73,428.551 1870.55,428.556 1872.38,428.56 1874.21,428.563 1876.03,428.562 1877.86,428.558 \n",
       "  1879.69,428.552 1881.51,428.548 1883.34,428.544 1885.17,428.542 1886.99,428.542 1888.82,428.545 1890.65,428.548 1892.47,428.553 1894.3,428.558 1896.12,428.562 \n",
       "  1897.95,428.563 1899.78,428.56 1901.6,428.555 1903.43,428.55 1905.26,428.546 1907.08,428.543 1908.91,428.542 1910.74,428.543 1912.56,428.546 1914.39,428.551 \n",
       "  1916.22,428.556 1918.04,428.56 1919.87,428.563 1921.7,428.562 1923.52,428.557 1925.35,428.552 1927.18,428.548 1929,428.544 1930.83,428.542 1932.66,428.542 \n",
       "  1934.48,428.545 1936.31,428.549 1938.13,428.553 1939.96,428.558 1941.79,428.562 1943.61,428.563 1945.44,428.56 1947.27,428.555 1949.09,428.55 1950.92,428.545 \n",
       "  1952.75,428.543 1954.57,428.542 1956.4,428.543 1958.23,428.546 1960.05,428.551 1961.88,428.556 1963.71,428.56 1965.53,428.563 1967.36,428.561 1969.19,428.557 \n",
       "  1971.01,428.552 1972.84,428.547 1974.67,428.544 1976.49,428.542 1978.32,428.542 1980.14,428.545 1981.97,428.549 1983.8,428.554 1985.62,428.558 1987.45,428.562 \n",
       "  1989.28,428.563 1991.1,428.559 1992.93,428.555 1994.76,428.55 1996.58,428.545 1998.41,428.543 2000.24,428.542 2002.06,428.543 2003.89,428.547 2005.72,428.551 \n",
       "  2007.54,428.556 2009.37,428.56 2011.2,428.563 2013.02,428.561 2014.85,428.557 2016.68,428.552 2018.5,428.547 2020.33,428.544 2022.15,428.542 2023.98,428.543 \n",
       "  2025.81,428.545 2027.63,428.549 2029.46,428.554 2031.29,428.559 2033.11,428.562 2034.94,428.563 2036.77,428.559 2038.59,428.554 2040.42,428.549 2042.25,428.545 \n",
       "  2044.07,428.543 2045.9,428.542 2047.73,428.544 2049.55,428.547 2051.38,428.551 2053.21,428.556 2055.03,428.561 2056.86,428.563 2058.69,428.561 2060.51,428.557 \n",
       "  2062.34,428.552 2064.16,428.547 2065.99,428.544 2067.82,428.542 2069.64,428.543 2071.47,428.545 2073.3,428.549 2075.12,428.554 2076.95,428.559 2078.78,428.562 \n",
       "  2080.6,428.562 2082.43,428.559 2084.26,428.554 2086.08,428.549 2087.91,428.545 2089.74,428.543 2091.56,428.542 2093.39,428.544 2095.22,428.547 2097.04,428.552 \n",
       "  2098.87,428.557 2100.7,428.561 2102.52,428.563 2104.35,428.561 2106.18,428.557 2108,428.551 2109.83,428.547 2111.65,428.544 2113.48,428.542 2115.31,428.543 \n",
       "  2117.13,428.545 2118.96,428.549 2120.79,428.554 2122.61,428.559 2124.44,428.562 2126.27,428.562 2128.09,428.559 2129.92,428.554 2131.75,428.549 2133.57,428.545 \n",
       "  2135.4,428.543 2137.23,428.542 2139.05,428.544 2140.88,428.547 2142.71,428.552 2144.53,428.557 2146.36,428.561 2148.19,428.563 2150.01,428.561 2151.84,428.556 \n",
       "  2153.66,428.551 2155.49,428.547 2157.32,428.543 2159.14,428.542 2160.97,428.543 2162.8,428.545 2164.62,428.549 2166.45,428.554 2168.28,428.559 2170.1,428.562 \n",
       "  2171.93,428.562 2173.76,428.559 2175.58,428.554 2177.41,428.549 2179.24,428.545 2181.06,428.542 2182.89,428.542 2184.72,428.544 2186.54,428.547 2188.37,428.552 \n",
       "  2190.2,428.557 2192.02,428.561 2193.85,428.563 2195.67,428.561 2197.5,428.556 2199.33,428.551 2201.15,428.547 2202.98,428.543 2204.81,428.542 2206.63,428.543 \n",
       "  2208.46,428.545 2210.29,428.55 2212.11,428.555 2213.94,428.559 2215.77,428.562 2217.59,428.562 2219.42,428.559 2221.25,428.554 2223.07,428.549 2224.9,428.545 \n",
       "  2226.73,428.542 2228.55,428.542 2230.38,428.544 2232.21,428.547 2234.03,428.552 2235.86,428.557 2237.68,428.561 2239.51,428.563 2241.34,428.561 2243.16,428.556 \n",
       "  2244.99,428.551 2246.82,428.546 2248.64,428.543 2250.47,428.542 2252.3,428.543 2254.12,428.546 2255.95,428.55 2257.78,428.555 2259.6,428.559 2261.43,428.562 \n",
       "  2263.26,428.562 2265.08,428.558 2266.91,428.553 2268.74,428.548 2270.56,428.545 2272.39,428.542 2274.22,428.542 2276.04,428.544 2277.87,428.548 2279.69,428.552 \n",
       "  2281.52,428.557 2283.35,428.561 2285.17,428.563 2287,428.56 2288.83,428.556 2290.65,428.551 2292.48,428.546 2294.31,428.543 2296.13,428.542 2297.96,428.543 \n",
       "  2299.79,428.546 2301.61,428.55 2303.44,428.555 2305.27,428.56 2307.09,428.562 2308.92,428.562 2310.75,428.558 2312.57,428.553 2314.4,428.548 2316.23,428.544 \n",
       "  2318.05,428.542 2319.88,428.542 2321.7,428.544 2323.53,428.548 2325.36,428.552 2327.18,428.557 2329.01,428.561 2330.84,428.563 2332.66,428.56 2334.49,428.557 \n",
       "  2336.32,428.553 2338.14,428.55 2339.97,428.548 2341.8,428.547 2343.62,428.548 2345.45,428.55 2347.28,428.553 2349.1,428.556 2350.93,428.558 2352.76,428.558 \n",
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      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "initialState = LVector(S=999, E=1, H=1, I=1, R=0);\n",
    "params = LVector(inf=0.002, postLatency=0.4, rec=0.2, waning=0.03);\n",
    "prob = ODEProblem(vectorfield(seirsTreatmentMediated),initialState,(0.0,500.0),params);\n",
    "sol = solve(prob,Tsit5(),abstol=1e-8);\n",
    "plot(sol)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "484d2d64",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div class=\"c-set\">\n",
       "<span class=\"c-set-summary\">LabelledPetriNet with elements T = 1:3, S = 1:4, I = 1:4, O = 1:4</span>\n",
       "<table>\n",
       "  <thead>\n",
       "    <tr class = \"header headerLastRow\">\n",
       "      <th class = \"rowNumber\">T</th>\n",
       "      <th style = \"text-align: right;\">tname</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td class = \"rowNumber\">1</td>\n",
       "      <td style = \"text-align: right;\">vacc</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td class = \"rowNumber\">2</td>\n",
       "      <td style = \"text-align: right;\">wane1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td class = \"rowNumber\">3</td>\n",
       "      <td style = \"text-align: right;\">wane2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<table>\n",
       "  <thead>\n",
       "    <tr class = \"header headerLastRow\">\n",
       "      <th class = \"rowNumber\">S</th>\n",
       "      <th style = \"text-align: right;\">sname</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td class = \"rowNumber\">1</td>\n",
       "      <td style = \"text-align: right;\">S</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td class = \"rowNumber\">2</td>\n",
       "      <td style = \"text-align: right;\">H</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td class = \"rowNumber\">3</td>\n",
       "      <td style = \"text-align: right;\">VFull</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td class = \"rowNumber\">4</td>\n",
       "      <td style = \"text-align: right;\">VPartial</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<table>\n",
       "  <thead>\n",
       "    <tr class = \"header headerLastRow\">\n",
       "      <th class = \"rowNumber\">I</th>\n",
       "      <th style = \"text-align: right;\">it</th>\n",
       "      <th style = \"text-align: right;\">is</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td class = \"rowNumber\">1</td>\n",
       "      <td style = \"text-align: right;\">1</td>\n",
       "      <td style = \"text-align: right;\">1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td class = \"rowNumber\">2</td>\n",
       "      <td style = \"text-align: right;\">1</td>\n",
       "      <td style = \"text-align: right;\">2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td class = \"rowNumber\">3</td>\n",
       "      <td style = \"text-align: right;\">2</td>\n",
       "      <td style = \"text-align: right;\">3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td class = \"rowNumber\">4</td>\n",
       "      <td style = \"text-align: right;\">3</td>\n",
       "      <td style = \"text-align: right;\">4</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<table>\n",
       "  <thead>\n",
       "    <tr class = \"header headerLastRow\">\n",
       "      <th class = \"rowNumber\">O</th>\n",
       "      <th style = \"text-align: right;\">ot</th>\n",
       "      <th style = \"text-align: right;\">os</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td class = \"rowNumber\">1</td>\n",
       "      <td style = \"text-align: right;\">1</td>\n",
       "      <td style = \"text-align: right;\">3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td class = \"rowNumber\">2</td>\n",
       "      <td style = \"text-align: right;\">1</td>\n",
       "      <td style = \"text-align: right;\">2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td class = \"rowNumber\">3</td>\n",
       "      <td style = \"text-align: right;\">2</td>\n",
       "      <td style = \"text-align: right;\">4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td class = \"rowNumber\">4</td>\n",
       "      <td style = \"text-align: right;\">3</td>\n",
       "      <td style = \"text-align: right;\">1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>\n"
      ],
      "text/plain": [
       "LabelledPetriNet with elements T = 1:3, S = 1:4, I = 1:4, O = 1:4\n",
       "┌───┬───────┐\n",
       "│\u001b[1m T \u001b[0m│\u001b[1m tname \u001b[0m│\n",
       "├───┼───────┤\n",
       "│ 1 │  vacc │\n",
       "│ 2 │ wane1 │\n",
       "│ 3 │ wane2 │\n",
       "└───┴───────┘\n",
       "┌───┬──────────┐\n",
       "│\u001b[1m S \u001b[0m│\u001b[1m    sname \u001b[0m│\n",
       "├───┼──────────┤\n",
       "│ 1 │        S │\n",
       "│ 2 │        H │\n",
       "│ 3 │    VFull │\n",
       "│ 4 │ VPartial │\n",
       "└───┴──────────┘\n",
       "┌───┬────┬────┐\n",
       "│\u001b[1m I \u001b[0m│\u001b[1m it \u001b[0m│\u001b[1m is \u001b[0m│\n",
       "├───┼────┼────┤\n",
       "│ 1 │  1 │  1 │\n",
       "│ 2 │  1 │  2 │\n",
       "│ 3 │  2 │  3 │\n",
       "│ 4 │  3 │  4 │\n",
       "└───┴────┴────┘\n",
       "┌───┬────┬────┐\n",
       "│\u001b[1m O \u001b[0m│\u001b[1m ot \u001b[0m│\u001b[1m os \u001b[0m│\n",
       "├───┼────┼────┤\n",
       "│ 1 │  1 │  3 │\n",
       "│ 2 │  1 │  2 │\n",
       "│ 3 │  2 │  4 │\n",
       "│ 4 │  3 │  1 │\n",
       "└───┴────┴────┘\n"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vaccineHCWSimple = LabelledPetriNet([:S, :H, :VFull, :VPartial], :vacc=>((:S,:H)=>(:VFull,:H)), :wane1=>(:VFull=>:VPartial), :wane2=>(:VPartial=>:S))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "02c903fe",
   "metadata": {},
   "outputs": [
    {
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      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Graph(vaccineHCWSimple)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "8f6eb605",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<div class=\"c-set\">\n",
       "<span class=\"c-set-summary\">LabelledPetriNet with elements T = 1:3, S = 1:4, I = 1:4, O = 1:3</span>\n",
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       "      <td style = \"text-align: right;\">4</td>\n",
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      "text/plain": [
       "LabelledPetriNet with elements T = 1:3, S = 1:4, I = 1:4, O = 1:3\n",
       "┌───┬───────┐\n",
       "│\u001b[1m T \u001b[0m│\u001b[1m tname \u001b[0m│\n",
       "├───┼───────┤\n",
       "│ 1 │  vacc │\n",
       "│ 2 │ wane1 │\n",
       "│ 3 │ wane2 │\n",
       "└───┴───────┘\n",
       "┌───┬──────────┐\n",
       "│\u001b[1m S \u001b[0m│\u001b[1m    sname \u001b[0m│\n",
       "├───┼──────────┤\n",
       "│ 1 │        S │\n",
       "│ 2 │        D │\n",
       "│ 3 │    VFull │\n",
       "│ 4 │ VPartial │\n",
       "└───┴──────────┘\n",
       "┌───┬────┬────┐\n",
       "│\u001b[1m I \u001b[0m│\u001b[1m it \u001b[0m│\u001b[1m is \u001b[0m│\n",
       "├───┼────┼────┤\n",
       "│ 1 │  1 │  1 │\n",
       "│ 2 │  1 │  2 │\n",
       "│ 3 │  2 │  3 │\n",
       "│ 4 │  3 │  4 │\n",
       "└───┴────┴────┘\n",
       "┌───┬────┬────┐\n",
       "│\u001b[1m O \u001b[0m│\u001b[1m ot \u001b[0m│\u001b[1m os \u001b[0m│\n",
       "├───┼────┼────┤\n",
       "│ 1 │  1 │  3 │\n",
       "│ 2 │  2 │  4 │\n",
       "│ 3 │  3 │  1 │\n",
       "└───┴────┴────┘\n"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vaccineDoseSimple = LabelledPetriNet([:S, :D, :VFull, :VPartial], :vacc=>((:S,:D)=>:VFull), :wane1=>(:VFull=>:VPartial), :wane2=>(:VPartial=>:S))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "803c7def",
   "metadata": {},
   "outputs": [
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       "Graph(\"G\", true, \"dot\", Catlab.Graphics.Graphviz.Statement[Catlab.Graphics.Graphviz.Node(\"s1\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"S\", :shape => \"circle\", :color => \"#6C9AC3\", :pos => \"\")), Catlab.Graphics.Graphviz.Node(\"s2\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"D\", :shape => \"circle\", :color => \"#6C9AC3\", :pos => \"\")), Catlab.Graphics.Graphviz.Node(\"s3\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"VFull\", :shape => \"circle\", :color => \"#6C9AC3\", :pos => \"\")), Catlab.Graphics.Graphviz.Node(\"s4\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"VPartial\", :shape => \"circle\", :color => \"#6C9AC3\", :pos => \"\")), Catlab.Graphics.Graphviz.Node(\"t1\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"vacc\", :shape => \"square\", :color => \"#E28F41\", :pos => \"\")), Catlab.Graphics.Graphviz.Node(\"t2\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"wane1\", :shape => \"square\", :color => \"#E28F41\", :pos => \"\")), Catlab.Graphics.Graphviz.Node(\"t3\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"wane2\", :shape => \"square\", :color => \"#E28F41\", :pos => \"\")), Catlab.Graphics.Graphviz.Edge(Catlab.Graphics.Graphviz.NodeID[Catlab.Graphics.Graphviz.NodeID(\"s3\", \"\", \"\"), Catlab.Graphics.Graphviz.NodeID(\"t2\", \"\", \"\")], OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:labelfontsize => \"6\", :label => \"1\")), Catlab.Graphics.Graphviz.Edge(Catlab.Graphics.Graphviz.NodeID[Catlab.Graphics.Graphviz.NodeID(\"s4\", \"\", \"\"), Catlab.Graphics.Graphviz.NodeID(\"t3\", \"\", \"\")], OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:labelfontsize => \"6\", :label => \"1\")), Catlab.Graphics.Graphviz.Edge(Catlab.Graphics.Graphviz.NodeID[Catlab.Graphics.Graphviz.NodeID(\"t1\", \"\", \"\"), Catlab.Graphics.Graphviz.NodeID(\"s3\", \"\", \"\")], OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:labelfontsize => \"6\", :label => \"1\")), Catlab.Graphics.Graphviz.Edge(Catlab.Graphics.Graphviz.NodeID[Catlab.Graphics.Graphviz.NodeID(\"t3\", \"\", \"\"), Catlab.Graphics.Graphviz.NodeID(\"s1\", \"\", \"\")], OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:labelfontsize => \"6\", :label => \"1\")), Catlab.Graphics.Graphviz.Edge(Catlab.Graphics.Graphviz.NodeID[Catlab.Graphics.Graphviz.NodeID(\"t2\", \"\", \"\"), Catlab.Graphics.Graphviz.NodeID(\"s4\", \"\", \"\")], OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:labelfontsize => \"6\", :label => \"1\")), Catlab.Graphics.Graphviz.Edge(Catlab.Graphics.Graphviz.NodeID[Catlab.Graphics.Graphviz.NodeID(\"s2\", \"\", \"\"), Catlab.Graphics.Graphviz.NodeID(\"t1\", \"\", \"\")], OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:labelfontsize => \"6\", :label => \"1\")), Catlab.Graphics.Graphviz.Edge(Catlab.Graphics.Graphviz.NodeID[Catlab.Graphics.Graphviz.NodeID(\"s1\", \"\", \"\"), Catlab.Graphics.Graphviz.NodeID(\"t1\", \"\", \"\")], OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:labelfontsize => \"6\", :label => \"1\"))], OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:rankdir => \"LR\"), OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:shape => \"plain\", :style => \"filled\", :color => \"white\"), OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:splines => \"splines\"))"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Graph(vaccineDoseSimple)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "52c853e5",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<div class=\"c-set\">\n",
       "<span class=\"c-set-summary\">LabelledPetriNet with elements T = 1:3, S = 1:5, I = 1:5, O = 1:4</span>\n",
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       "  <thead>\n",
       "    <tr class = \"header headerLastRow\">\n",
       "      <th class = \"rowNumber\">T</th>\n",
       "      <th style = \"text-align: right;\">tname</th>\n",
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       "    <tr>\n",
       "      <td class = \"rowNumber\">2</td>\n",
       "      <td style = \"text-align: right;\">wane1</td>\n",
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       "      <td style = \"text-align: right;\">wane2</td>\n",
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       "  </tbody>\n",
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       "  <thead>\n",
       "    <tr class = \"header headerLastRow\">\n",
       "      <th class = \"rowNumber\">S</th>\n",
       "      <th style = \"text-align: right;\">sname</th>\n",
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       "      <td class = \"rowNumber\">1</td>\n",
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       "      <td class = \"rowNumber\">2</td>\n",
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       "    <tr>\n",
       "      <td class = \"rowNumber\">3</td>\n",
       "      <td style = \"text-align: right;\">D</td>\n",
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       "    <tr>\n",
       "      <td class = \"rowNumber\">4</td>\n",
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       "    <tr>\n",
       "      <td class = \"rowNumber\">5</td>\n",
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       "  <thead>\n",
       "    <tr class = \"header headerLastRow\">\n",
       "      <th class = \"rowNumber\">I</th>\n",
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      "text/plain": [
       "LabelledPetriNet with elements T = 1:3, S = 1:5, I = 1:5, O = 1:4\n",
       "┌───┬───────┐\n",
       "│\u001b[1m T \u001b[0m│\u001b[1m tname \u001b[0m│\n",
       "├───┼───────┤\n",
       "│ 1 │  vacc │\n",
       "│ 2 │ wane1 │\n",
       "│ 3 │ wane2 │\n",
       "└───┴───────┘\n",
       "┌───┬──────────┐\n",
       "│\u001b[1m S \u001b[0m│\u001b[1m    sname \u001b[0m│\n",
       "├───┼──────────┤\n",
       "│ 1 │        S │\n",
       "│ 2 │        H │\n",
       "│ 3 │        D │\n",
       "│ 4 │    VFull │\n",
       "│ 5 │ VPartial │\n",
       "└───┴──────────┘\n",
       "┌───┬────┬────┐\n",
       "│\u001b[1m I \u001b[0m│\u001b[1m it \u001b[0m│\u001b[1m is \u001b[0m│\n",
       "├───┼────┼────┤\n",
       "│ 1 │  1 │  1 │\n",
       "│ 2 │  1 │  3 │\n",
       "│ 3 │  1 │  2 │\n",
       "│ 4 │  2 │  4 │\n",
       "│ 5 │  3 │  5 │\n",
       "└───┴────┴────┘\n",
       "┌───┬────┬────┐\n",
       "│\u001b[1m O \u001b[0m│\u001b[1m ot \u001b[0m│\u001b[1m os \u001b[0m│\n",
       "├───┼────┼────┤\n",
       "│ 1 │  1 │  4 │\n",
       "│ 2 │  1 │  2 │\n",
       "│ 3 │  2 │  5 │\n",
       "│ 4 │  3 │  1 │\n",
       "└───┴────┴────┘\n"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vaccineHCWDoseSimple = LabelledPetriNet([:S, :H, :D, :VFull, :VPartial], :vacc=>((:S,:D, :H)=>(:VFull, :H)), :wane1=>(:VFull=>:VPartial), :wane2=>(:VPartial=>:S))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "c3595c57",
   "metadata": {},
   "outputs": [
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      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Graph(vaccineHCWDoseSimple)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "0518a8fa",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<div class=\"c-set\">\n",
       "<span class=\"c-set-summary\">LabelledPetriNet with elements T = 1:2, S = 1:3, I = 1:2, O = 1:2</span>\n",
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       "    <tr class = \"header headerLastRow\">\n",
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       "      <td class = \"rowNumber\">2</td>\n",
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       "  </tbody>\n",
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       "<table>\n",
       "  <thead>\n",
       "    <tr class = \"header headerLastRow\">\n",
       "      <th class = \"rowNumber\">S</th>\n",
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       "      <th style = \"text-align: right;\">it</th>\n",
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      "text/plain": [
       "LabelledPetriNet with elements T = 1:2, S = 1:3, I = 1:2, O = 1:2\n",
       "┌───┬───────┐\n",
       "│\u001b[1m T \u001b[0m│\u001b[1m tname \u001b[0m│\n",
       "├───┼───────┤\n",
       "│ 1 │ wane1 │\n",
       "│ 2 │ wane2 │\n",
       "└───┴───────┘\n",
       "┌───┬──────────┐\n",
       "│\u001b[1m S \u001b[0m│\u001b[1m    sname \u001b[0m│\n",
       "├───┼──────────┤\n",
       "│ 1 │        S │\n",
       "│ 2 │    VFull │\n",
       "│ 3 │ VPartial │\n",
       "└───┴──────────┘\n",
       "┌───┬────┬────┐\n",
       "│\u001b[1m I \u001b[0m│\u001b[1m it \u001b[0m│\u001b[1m is \u001b[0m│\n",
       "├───┼────┼────┤\n",
       "│ 1 │  1 │  2 │\n",
       "│ 2 │  2 │  3 │\n",
       "└───┴────┴────┘\n",
       "┌───┬────┬────┐\n",
       "│\u001b[1m O \u001b[0m│\u001b[1m ot \u001b[0m│\u001b[1m os \u001b[0m│\n",
       "├───┼────┼────┤\n",
       "│ 1 │  1 │  3 │\n",
       "│ 2 │  2 │  1 │\n",
       "└───┴────┴────┘\n"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vaccineWaning = LabelledPetriNet([:S, :VFull, :VPartial], :wane1=>(:VFull=>:VPartial), :wane2=>(:VPartial=>:S))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "fccbf434",
   "metadata": {},
   "outputs": [
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       "Graph(\"G\", true, \"dot\", Catlab.Graphics.Graphviz.Statement[Catlab.Graphics.Graphviz.Node(\"s1\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"S\", :shape => \"circle\", :color => \"#6C9AC3\", :pos => \"\")), Catlab.Graphics.Graphviz.Node(\"s2\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"VFull\", :shape => \"circle\", :color => \"#6C9AC3\", :pos => \"\")), Catlab.Graphics.Graphviz.Node(\"s3\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"VPartial\", :shape => \"circle\", :color => \"#6C9AC3\", :pos => \"\")), Catlab.Graphics.Graphviz.Node(\"t1\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"wane1\", :shape => \"square\", :color => \"#E28F41\", :pos => \"\")), Catlab.Graphics.Graphviz.Node(\"t2\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"wane2\", :shape => \"square\", :color => \"#E28F41\", :pos => \"\")), Catlab.Graphics.Graphviz.Edge(Catlab.Graphics.Graphviz.NodeID[Catlab.Graphics.Graphviz.NodeID(\"s3\", \"\", \"\"), Catlab.Graphics.Graphviz.NodeID(\"t2\", \"\", \"\")], OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:labelfontsize => \"6\", :label => \"1\")), Catlab.Graphics.Graphviz.Edge(Catlab.Graphics.Graphviz.NodeID[Catlab.Graphics.Graphviz.NodeID(\"t2\", \"\", \"\"), Catlab.Graphics.Graphviz.NodeID(\"s1\", \"\", \"\")], OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:labelfontsize => \"6\", :label => \"1\")), Catlab.Graphics.Graphviz.Edge(Catlab.Graphics.Graphviz.NodeID[Catlab.Graphics.Graphviz.NodeID(\"t1\", \"\", \"\"), Catlab.Graphics.Graphviz.NodeID(\"s3\", \"\", \"\")], OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:labelfontsize => \"6\", :label => \"1\")), Catlab.Graphics.Graphviz.Edge(Catlab.Graphics.Graphviz.NodeID[Catlab.Graphics.Graphviz.NodeID(\"s2\", \"\", \"\"), Catlab.Graphics.Graphviz.NodeID(\"t1\", \"\", \"\")], OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:labelfontsize => \"6\", :label => \"1\"))], OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:rankdir => \"LR\"), OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:shape => \"plain\", :style => \"filled\", :color => \"white\"), OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:splines => \"splines\"))"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Graph(vaccineWaning)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "fcb21689",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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