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

Dramane OUEDRAOGO; Idrissa       IBRANGO; Aboudramane GUIRO

doi:10.26637/mjm1002/004

Abstract

The aim of this work is to study the dynamics of a reaction-diffusion SIR epidemic model with a nonlinear general incidence 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.

Keywords:

SIR epidemic models, HBV model, immune, general incidence function, global stability, Lyapunov functional, reaction-diffusion

Mathematics Subject Classification:

65L03, 65L03, 34D20, 34D23

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Dramane OUEDRAOGO Départment de Mathématique, Centre Universitaire de Banfora, Université Nazi BONI, Burkina Faso.
Idrissa IBRANGO Départment de Mathématique,Université Nazi BONI, Burkina Faso.
Aboudramane GUIRO Départment de Mathématique,Université Nazi BONI, Burkina Faso.

Pages: 139-150
Date Published: 01-04-2022
Vol. 10 No. 02 (2022): Malaya Journal of Matematik (MJM)

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