Stochastic and deterministic SIS patch model

Ténan Yeo (1)

1 CUIMC - Columbia University Irving Medical Center

Here, we consider an SIS epidemic model where the individuals are distributed on several distinct patches. We construct a stochastic model and then prove that it converges to a deterministic model as the total population size tends to infinity. We next study the equilibria of the deterministic model. Our main contribution is a stability result of the endemic equilibrium in the case \begin{document}$ \mathcal{R}_0>1 $\end{document}. Finally we compare the equilibria with those of the homogeneous model, and with those of isolated patches.

Domains: Mathematics [math]

Ténan Yeo. Stochastic and deterministic SIS patch model. Discrete and Continuous Dynamical Systems - Series B, 2021, 26 (12), pp.6173. ⟨10.3934/dcdsb.2021012⟩. ⟨hal-03663217⟩