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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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Journal articles
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https://hal-amu.archives-ouvertes.fr/hal-03663217
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Submitted on : Tuesday, May 10, 2022 - 1:17:51 AM
Last modification on : Tuesday, May 10, 2022 - 9:16:40 AM

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### Citation

TÃ©nan 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⟩

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