General models of host-parasite systems. Global analysis

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July 2007, 8(1): 1-17. doi: 10.3934/dcdsb.2007.8.1

General models of host-parasite systems. Global analysis

P. Adda ^1, , J. L. Dimi ^1, , A. Iggidir ^1, , J. C. Kamgang ^1, , G. Sallet ^1, and J. J. Tewa ^1,

1.	INRIA-Lorraine and University Paul Verlaine-Metz, LMAM-CNRS UMR 7122, ISGMP Bat. A, Ile du Saulcy, 57045 Metz Cedex 01, France, France, France, France, France, France

Received October 2005 Revised February 2006 Published April 2007

Abstract
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We obtain global stability results for within-host models with $k$ age-class of parasitized cells and two strains of parasites. The stability is determined by the value of the basic reproduction ratio $\mathcal R_0$. A competitive exclusion principle holds. This means that if $\mathcal R_0 >1$ generically an unique equilibrium, corresponding to the extinction of one strain and the survival of the other strain, is globally asymptotically stable on the positive orthant.

Keywords: Plasmodium falciparum, global stability, Nonlinear dynamical systems, coexistence., malaria models.

Mathematics Subject Classification: Primary: 34D23, 34A34; Secondary: 92D3.

Citation: P. Adda, J. L. Dimi, A. Iggidir, J. C. Kamgang, G. Sallet, J. J. Tewa. General models of host-parasite systems. Global analysis. Discrete & Continuous Dynamical Systems - B, 2007, 8 (1) : 1-17. doi: 10.3934/dcdsb.2007.8.1

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