American Institute of Mathematical Sciences

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2007, 2007(Special): 506-519. doi: 10.3934/proc.2007.2007.506

Multi-compartment models

Abderrahman Iggidr 1, , Josepha Mbang 2, , Gauthier Sallet 1, and  Jean-Jules Tewa 2,

1. 

Laboratoire de Mathématiques et Applications, UMR CNRS 7122, University of Metz and INRIA Lorraine, Metz, France, France
2. 

University of Yaoundé I, Cameroon, Cameroon

Received  September 2006 Revised  June 2007 Published  September 2007

We consider models with a general structure which, for example, encompasses the so-called DI, SP or DISP models with mass action incidence. We give a very simple formule for the basic reproduction ratio $R_0$. If $R_0 \<= 1$ we prove that the disease free equilibrium is globally asymptotically stable on the nonnegative orthant. If $R_0$ > 1, we prove the existence of a unique endemic equilibrium in the positive orthant and give an explicit formula. We prove the global asymptotic stability of the endemic equilibrium, when $R_0$ > 1 for SP model.
Keywords: Nonlinear dynamical systems, global stability., epidemic models.
Mathematics Subject Classification: 34D23, 34A34, 92D3.
Citation: Abderrahman Iggidr, Josepha Mbang, Gauthier Sallet, Jean-Jules Tewa. Multi-compartment models. Conference Publications, 2007, 2007 (Special) : 506-519. doi: 10.3934/proc.2007.2007.506
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