American Institute of Mathematical Sciences

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2008, 5(1): 20-33. doi: 10.3934/mbe.2008.5.20

Global stability analysis for SEIS models with n latent classes

Napoleon Bame 1, , Samuel Bowong 2, , Josepha Mbang 3, , Gauthier Sallet 4, and  Jean-Jules Tewa 3,

1. 

Department of Mathematics and Computer Science, University of Dschang, Cameroon
2. 

Department of Mathematics, University of Douala, Cameroon
3. 

University of Yaoundé I
4. 

Laboratoire de Mathématiques et Applications, UMR CNRS 7122, University of Metz and INRIA Lorraine, Metz

Received  October 2006 Revised  June 2007 Published  January 2008

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.
Keywords: nonlinear dynamical systems, epidemic models, global stability..
Mathematics Subject Classification: 34D23, 34A34, 92D3.
Citation: Napoleon Bame, Samuel Bowong, Josepha Mbang, Gauthier Sallet, Jean-Jules Tewa. Global stability analysis for SEIS models with n latent classes. Mathematical Biosciences & Engineering, 2008, 5 (1) : 20-33. doi: 10.3934/mbe.2008.5.20
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