Global Analysis of New Malaria Intrahost Models with a Competitive Exclusion Principle

Abderrahman Iggidr 1, * Jean-Claude Kamgang 2 Gauthier Sallet 1 Jean-Jules Tewa 1, 3
* Auteur correspondant
1 MASAIE - Tools and models of nonlinear control theory for epidemiology and immunology
LMAM - Laboratoire de Mathématiques et Applications de Metz, Inria Nancy - Grand Est, IECL - Institut Élie Cartan de Lorraine
Abstract : In this paper we propose a malaria within-host model with k classes of age for the parasitized red blood cells and n strains for the parasite. We provide a global analysis for this model. A competitive exclusion principle holds. If R0, the basic reproduction number, satisfies R0 ≤ 1, then the disease-free equilibrium is globally asymptotically stable. On the contrary if R0 > 1, then generically there is a unique endemic equilibrium which corresponds to the endemic stabilization of the most virulent parasite strain and to the extinction of all the other parasites strains. We prove that this equilibrium is globally asymptotically stable on the positive orthant if a mild sufficient condition is satisfied.
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SIAM Journal on Applied Mathematics, Society for Industrial and Applied Mathematics, 2006, 67 (1), pp.260-278. 〈http://siamdl.aip.org/dbt/dbt.jsp?KEY=SMJMAP&Volume=67&Issue=1〉. 〈10.1137/050643271〉
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Abderrahman Iggidr, Jean-Claude Kamgang, Gauthier Sallet, Jean-Jules Tewa. Global Analysis of New Malaria Intrahost Models with a Competitive Exclusion Principle. SIAM Journal on Applied Mathematics, Society for Industrial and Applied Mathematics, 2006, 67 (1), pp.260-278. 〈http://siamdl.aip.org/dbt/dbt.jsp?KEY=SMJMAP&Volume=67&Issue=1〉. 〈10.1137/050643271〉. 〈inria-00552014〉

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