Global stability analysis for SEIS models with n latent classes

Napoleon Bame; Samuel Bowong; Josepha Mbang; Gauthier Sallet; Jean-Jules Tewa

doi:10.3934/mbe.2008.5.20

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2008, Volume 5, Issue 1: 20-33. Doi: 10.3934/mbe.2008.5.20

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Global stability analysis for SEIS models with n latent classes

1.
Department of Mathematics and Computer Science, University of Dschang
2.
Department of Mathematics, University of Douala
3.
University of Yaoundé I
4.
Laboratoire de Mathématiques et Applications, UMR CNRS 7122, University of Metz and INRIA Lorraine, Metz

Received: September 30, 2006

Revised: May 31, 2007

Published: December 2007

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Abstract

We compute the basic reproduction ratio of a SEIS model with n classes of latent individuals and bilinear incidence.The system exhibits the traditional behaviour. We prove that if R0 ≤1, then the disease-free equilibrium is globally asymptotically stable on the nonnegative orthant and if R0 > 1, an endemic equilibrium exists and is globally asymptotically stable on the positive orthant.

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Mathematics Subject Classification: 34D23, 34A34, 92D30.

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