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Multi-compartment models

Pages: 506 - 519, Issue Special, September 2007

 Abstract        Full Text (216.5K)              

Abderrahman Iggidr - Laboratoire de Mathématiques et Applications, UMR CNRS 7122, University of Metz and INRIA Lorraine, Metz, France (email)
Josepha Mbang - University of Yaoundé I, Cameroon (email)
Gauthier Sallet - Laboratoire de Mathématiques et Applications, UMR CNRS 7122, University of Metz and INRIA Lorraine, Metz, France (email)
Jean-Jules Tewa - University of Yaoundé I, Cameroon (email)

Abstract: 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, epidemic models, global stability.
Mathematics Subject Classification:  34D23, 34A34, 92D30.

Received: September 2006;      Revised: June 2007;      Published: September 2007.