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Diffusive Model Reproducing the Spread of COVID-19

This repository rises as an undergraduate project to reproduce the main article's results "Diffusion as a first model of spread of viral infection". On the other hand, this is my version using C/C++ because original project is made using Python, and it can be found in DiffusiveSIR, where I worked with more people.

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Behind the code

Before to explain how to run the code, here are some details to understand the algorithm behind it. There are two principal ideas behind the spread of disease as a SIR model (Susceptible-Infected-Recovered model):

1. Diffusive movement of every individual:

We initialize simulation for a system of N non-interacting particles (populace) with the same diffusion constant D, a fraction of the initial population to be infected, and population density p, these define domain dimensions, i.e., a square of L=sqrt(N/p). Then each particle is assigned to a uniform random position inside the domain. And one can simulate the diffusion of a particle from its previous position by generating a Gaussian distribution of zero mean and variance 2Dt.

2. Spread of disease within the code:

Here appears specific-simulation variables. Thus at each step, namely, every time we move the whole system, each susceptible individual has the same probability to get sick if it is found whitin a distance less than transmision ratio, because of this it can get sick. Finally, population just can be infected for 14 days (in this case, but all these variable can be modified), so when this time is up individuals get recovered (which means really are recovered or dead).

A different colour depicts the state of every particle.

  • Green: Susceptible (it could get sick)
  • Red: Infected
  • Yellow: Recovered (really recovered or dead)

Running the Code

To get the SIR curves, run the makefile:

  make

This file contains information about all variables which are by default (these values are taken from main article to reproduce the spread in New York), where one can find:

  • N = 100 (number of non-interacting particles)
  • Inf = 0.011 (fraction of the initial population to be infected)
  • den = 0.012 (population density)
  • D = 100 (diffusive constant)
  • dt = 0.01 (time spet of evolution)
  • r_t = 14.0 (maximum period to be infected and spreed the disease)
  • i_d = 2.0 (transmision ratio in meter)
  • i_p = 0.2 (probability to get infected) Any of these can be easly modified by performing (e.g. diffusive constant):
  make "D"=452 "other_variable"=value ...

To get the initial gif just run:

  make gif

The data and images going to be alocated in data directory.

Slight comparision of results

This algorithm was run for New York values such as the main article does. So we find:

First two images are from simulation for N=100 and N=1000, the last one is from the original article, this for New York city.