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Article Dans Une Revue Journal of Differential Equations Année : 2022

An Infinite-Dimensional Metapopulation SIS Model

Un modèle SIS en dimension infinie

Résumé

In this article, we introduce an infinite-dimensional deterministic SIS model which takes into account the heterogeneity of the infections and the social network among a large population. We study the long-time behavior of the dynamic. We identify the basic reproduction number $R_0$ which determines whether there exists a stable endemic steady state (super-critical case: $R_0>1$) or if the only equilibrium is disease-free (critical and sub-critical case: $R_0\leq1$). As an application of this general study, we prove that the so-called ``leaky'' and ``all-or-nothing'' vaccination mechanism have the same effect on $R_0$. This framework is also very natural and intuitive to model lockdown policies and study their impact.
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Dates et versions

hal-02867615 , version 1 (14-06-2020)

Identifiants

Citer

Jean-François Delmas, Dylan Dronnier, Pierre-André Zitt. An Infinite-Dimensional Metapopulation SIS Model. Journal of Differential Equations, 2022, 313, pp.1-53. ⟨10.1016/j.jde.2021.12.024⟩. ⟨hal-02867615⟩
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