Global Stability of an Epidemic Model with Two Infected Stages and Mass-Action Incidence

Authors

  • Mamadou Lamine Diouf UFR de Sciences AppliquГ©es et Technologies de l'UniversitГ© Gaston BERGER- MASAIE Project Team, INRIA Grand-Est et UniversitГ© de Lorraine
  • Abderrahman Iggidr
  • Mamadou Sy

DOI:

https://doi.org/10.11145/j.biomath.2014.07.211

Keywords:

Epidemic model, Global Stability, Lyaponov function, PoincarГ©-Bendixson

Abstract

The goal of this paper is the establishment of the global asymptotic stability of the model SI with two classes of infected stages and with varying total population size. The incidence used is the mass-action incidence given by (...). Existence and uniqueness of the endemic equilibrium is established when the basic reproduction number is greater than one. A Lyapunov function is used to prove the stability of the disease free equilibrium, and the Poincarŕe-Bendixson theorem allows to prove the stability of the endemic equilibrium when it exists.

Author Biographies

Mamadou Lamine Diouf, UFR de Sciences AppliquГ©es et Technologies de l'UniversitГ© Gaston BERGER- MASAIE Project Team, INRIA Grand-Est et UniversitГ© de Lorraine

Abderrahman Iggidr

Mamadou Sy

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Published

2014-08-20

Issue

Section

Original Articles