Global stability for reaction-diffusion SIR model with general incidence function

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Résumé

The aim of this work is to study the dynamics of a reaction-diffusion SIR epidemic model with a nonlinear generalincidence function. The local stability of the disease-free equilibrium is obtained via characteristic equations. The global existence, positivity and boundedness of solutions for reaction-diffusion system with homogeneous Neumann boundary conditions are proved. We mainly use the technique of Lyapunov functional to establish the global stability of both disease-free and endemic equilibria. Numerical simulations are presented to illustrate our theoretical results by using a suitable discretization of the model.

Mots-clés

nonlinear incidence rate, global stability, disease-free equilibrium, endemic equilibrium, Lyapunov functional, homogeneous Neumann boundary conditions, epidemic dynamics