American Institute of Mathematical Sciences

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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

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 and Continuous Dynamical Systems - B, 2007, 8 (1) : 1-17. doi: 10.3934/dcdsb.2007.8.1
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