Analyse de modèles épidémiologiques : applications à des modèles parasitaires, à la fièvre hémorragique Ebola

Abstract : This work comprises two parts. It is a study of the dynamics of epidemiological models. The first part deals with malaria intra-host models with and without immunity. For models with immunity we give some results of the global stability by using techniques of dynamical systems (Lyapounov, LaSalle,...). For models with immunity, we improve the De Leenheer Smith conditions for R0 on the stability of the endemic equilibrium. The second part deals with stastical transmission models and models of the dynamics of the hemorragic fever . For wich we have data on the episodes statistique occured at Mbomo (Congo) and Kikwit (RDC). For the statistical transmission models we compute R0 for data with incomplete contacts (Mbomo) and data with complete contacts b(Kikwit). Lastly, a study on the global stability is done for the dynamic models.
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Jean-Luc Dimi. Analyse de modèles épidémiologiques : applications à des modèles parasitaires, à la fièvre hémorragique Ebola. Mathématiques générales [math.GM]. Université Paul Verlaine - Metz, 2006. Français. ⟨NNT : 2006METZ002S⟩. ⟨tel-01752469⟩

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