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Analyse de modèles épidémiologiques à plusieurs classes d'infectés : stabilité et observabilité

Mamadou Lamine Diouf 1, 2
2 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 : The aim of this thesis is to give an analysis of the global stability and the observability of some epidemiological models with several stages of infected. We have made successively the study of the global stability for some SI, SIS and an another SI models with two classes of infected. At the two last models, we have made again the study, for the authors who studied them gave an erronous analysis to the fondamental question of the global study of the endemic equilibrium. Indeed, the same mistake has been done on the two works. Thus, we have propose to make light on erronous supposition on which they based their study, then we have tried to make another analysis of the global stability of those models. After that, we have end by the observaibility study of a SI model with n classes of infected. We have determined the high gain observer for that model.
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Submitted on : Wednesday, January 4, 2017 - 3:23:47 AM
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Mamadou Lamine Diouf. Analyse de modèles épidémiologiques à plusieurs classes d'infectés : stabilité et observabilité. Mathématiques [math]. Université Gaston BERGER de Saint-Louis du Sénégal, 2016. Français. ⟨tel-01425907⟩

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