Global stability of an SIS epidemic model with general incidence function in a patchy environment

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Résumé

We investigate some analytical results for an SIS compartmental epidemic model that describes the propagation of a
disease in a population of individuals who can travel among n patches. The model is formulated as a system of ordinary differential
equations, with terms accounting for general incidence, recovery, birth, death, and travel between cities. The basic reproduction
number, R0 of the model is computed; and we show that it is the threshold dynamics between the persistence and the extinction of
the epidemic. Hence, we show that if R0 < 1, the disease-free equilibrium is locally and globally attractive while, the system is
uniformly persistent and admits a unique endemic equilibrium which is globally asymptotically stable if R0 > 1. An example of
two patches are studied, and we prove that the choice of incidence function can strongly impact the spread of the disease. Finally,
numerical examples are performed to illustrate some theoretical results.

Mots-clés

Patchy environment, general incidence function, reproduction number, stability, numerical simulations