Analyse globale des modèles épidémiologiques multi-compartimentaux : application à des modèles intra-hôtes de paludisme et de V.I.H

Abstract : In this thesis, we analyse intrahost models of malaria and H.I.V. These models are of relatively recent appearance and describe the dynamics of the various stages of the parasites, like their interaction with the host cells, in particular the red blood cells and the immunity effectors. During this decade, there was a considerable work on the mathematical modeling of plasmodium falciparum infection ; a review has been done by Molineaux and Dietz. Our work forms part of this effort of comprehension of the models of Anderson, May and Gupta. The study of these models aims three principal goals : to explain the observations by biologically convincing assumptions, to predict the impact of the interventions (for example the use of the anti-paludic drugs and impregnated mosquito nets) and to consider the parameters hidden (one of these parameters being size of the sequestered population of red blood cells). We analyze the stages progression and the differential infectivity models ; then we leave the original model of Anderson, May and Gupta to propose and analyze a general model having the double advantage of describing the dynamics of evolution of the red blood cells, as well as the stages of morphological evolution of the parasites inside the parasitized red blood cells ; to finish we analyze a model whose innovation compared to the precedent is the bond between the compartment of susceptibles and that of the infectious one. We establish in all the studied cases here the global asymptotic stability of the disease free equilibrium (DFE) when the basic reproduction ratio R0 1. What means that the disease naturally dies out. We also obtain for each model studied here, a condition for global asymptotic stability of the endemic equilibrium when R0 > 1. In certain cases, the principle of exclusive competition is also used to slice
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Jean Jules Tewa. Analyse globale des modèles épidémiologiques multi-compartimentaux : application à des modèles intra-hôtes de paludisme et de V.I.H. Mathématiques générales [math.GM]. Université Paul Verlaine - Metz, 2007. Français. ⟨NNT : 2007METZ010S⟩. ⟨tel-01748973⟩

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