# Modelling stochastic solutions for the general stochastic epidemic

I have found the deterministic solutions for the following system of differential equations:

$$s'(t) = -\beta s(t) i(t) \\ i'(t) = \beta s(t) i(t) -\gamma i(t)\\ r'(t) = \gamma i(t)$$

So the solution to the above differential equations hold when $$n \rightarrow \infty$$ but I want to model when $$n$$ is not $$\rightarrow \infty$$. I am using the general stochastic model with infectious periods following $$I \sim exp(\gamma)$$.

I understand the deterministic solution but how did the writer get the plot of $$\bar{I}_n(t)$$ where $$\bar{I}_n(t) = I(t)/n$$ ? • Without further information this question cannot be answered. There is not "the" stochastic solution! Feb 2, 2021 at 12:38
• It is where the infectious period follows an exponential distribution $I \sim exp(\gamma)$
– Math
Feb 2, 2021 at 12:42
• There is still much too few information. Maybe you intend a Markov chain in countinuous time, but you have to elaborate this. In the context of Covid 19 there are many groups which try to model the epidemic and to evaluate them. So what is your model? Feb 2, 2021 at 13:10