connecting the primer example with the ngm model use in this repo

Author: dinacmistry

docs/primer.md

@@ -110,12 +110,11 @@ From here we can decompose the system into transmission and transition component
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-Then the NGM $K$ can be computed as $K = -E'T\Sigma^{-1}E = \frac{1}{\gamma}\boldsymbol{\beta}$. This matches intuition that the number of new infections generated in group $i$ by an average infected individual in group $j$ should be $\beta_{ij}$ rescaled by the generation interval $\gamma^{-1}$.
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+Then the NGM $K$ can be computed as $K = -E'T\Sigma^{-1}E = \frac{1}{\gamma}\boldsymbol{\beta}$.
 
+## NGM model in this repository
 
+In this repository we utilized an NGM to model consecutive generations of new infections. In this case we made the simplifying assumptions that infections last exactly one generation and that generations have not overlap. The NGM can then be rescaled by the generation interval $\gamma^{-1}$ to be $K = \boldsymbol{\beta'}$, where the elements $\beta'_{ij}$ are the average number of new infections generated by an typical infected individual in group $j$ in group $i$ per generation.
 <!-- New infections in the high-risk group can be modeled as $\beta'_{HH}S_H I_H + \beta'_{HL}S_H I_L$, where $\beta'_{ij}$ is the number of infections generated by group $j$ in group $i$. Similarly, new infections in the low-risk group can be modeled as $\beta'_{LH}S_L I_H + \beta'_{LL}S_L I_L$. Assuming infectious individuals recover at some average constant rate $\gamma$ , we can write the differential equation for the infectious states as -->
 
 <!-- $\frac{dI_H}{dt} = \beta'_{HH}S_H I_H + \beta'_{HL}S_H I_L - \gamma I_H$ -->