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Stochastic and deterministic SIS patch model

Abstract : 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.
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Submitted on : Tuesday, May 10, 2022 - 1:17:51 AM
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Ténan yeo. Stochastic and deterministic SIS patch model. Discrete and Continuous Dynamical Systems - Series B, American Institute of Mathematical Sciences, 2021, 26 (12), pp.6173. ⟨10.3934/dcdsb.2021012⟩. ⟨hal-03663217⟩



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