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 $\bar{I}_n(t) = I(t)/n$ ?