1
$\begingroup$

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

enter image description here

Improve this question
$\endgroup$
4
  • $\begingroup$ Without further information this question cannot be answered. There is not "the" stochastic solution! $\endgroup$
    – Dieter Kadelka
    Feb 2, 2021 at 12:38
  • $\begingroup$ It is where the infectious period follows an exponential distribution $I \sim exp(\gamma)$ $\endgroup$
    – Math
    Feb 2, 2021 at 12:42
  • $\begingroup$ 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? $\endgroup$
    – Dieter Kadelka
    Feb 2, 2021 at 13:10
  • $\begingroup$ @DieterKadelka please look at my amended question. $\endgroup$
    – Math
    Feb 2, 2021 at 13:43

0

Reset to default

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Browse other questions tagged or ask your own question.