Global stability analysis for SEIS models with n latent classes

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

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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: 01 October 2006 Accepted: 29 June 2018 Published: 01 January 2008
MSC : 34D23, 34A34, 92D30.

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.
- nonlinear dynamical systems,
- epidemic models,
- global stability.
Citation: Napoleon Bame, Samuel Bowong, Josepha Mbang, Gauthier Sallet, Jean-Jules Tewa. Global stability analysis for SEIS models with n latent classes[J]. Mathematical Biosciences and Engineering, 2008, 5(1): 20-33. doi: 10.3934/mbe.2008.5.20

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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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