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Research Paper | Mathematics | Morocco | Volume 3 Issue 5, May 2014

Global Stability of a Susceptible-Infected-Recovered (SIR) Epidemic Model with Two Infectious Stages and Treatment

M. Elhia ^[2] | A.E. Laaroussi | M. Rachik ^[4] | Z. Rachik ^[2] | E. Labriji ^[2]

Abstract: In this paper; we study the global stability of an epidemic model that incorporates two infectious staged and treatment. The model allows for infected individuals on the second stage to move from treated to untreated class and vice-versa. The basic reproduction number R0 is computed. If R0<1; then the disease-free equilibrium (DFE) is globally asymptotically stable and the disease always dies out. If R0>1; then there exists a unique endemic equilibrium (EE). This endemic equilibrium is shown to be globally asymptotically stable; under certain parameters restriction. The proof of global stability utilizes a Lyapunov function. To illustrate the theoretical results; numerical simulations are also provided.

Keywords: global stability, SIR epidemic model, the basic reproduction number R0, Lyapunov function, numerical simulation

Edition: Volume 3 Issue 5, May 2014,

Pages: 114 - 121

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