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Riveau Gilles ; Gauthier Sallet ; Tendeng Lena - A transmission model of Bilharzia : A mathematical analysis of an heterogeneous model
arima:1954 - Revue Africaine de Recherche en Informatique et Mathématiques Appliquées, August 24, 2011, Volume 14 - 2011 - Special issue CARI'10 - https://doi.org/10.46298/arima.1954A transmission model of Bilharzia : A mathematical analysis of an heterogeneous modelArticle
- 1 Centre d’Infection et d’Immunité de Lille - INSERM U 1019 - UMR 9017 - UMR 8204
- 2 Tools and models of nonlinear control theory for epidemiology and immunology
- 3 Laboratoire de Mathématiques et Applications de Metz
- 4 Inria Nancy - Grand Est
- 5 Centre Inria de l'Université de Lorraine
We consider an heterogeneous model of transmission of bilharzia. We compute the basic reproduction ratio R 0. We prove that if R 0 < 1, then the disease free equilibrium is globally asymptotically stable. If R 0 > 1 then there exists an unique endemic equilibrium, which is globally asymptotically stable. We will then consider possible applications to real data
Source: HAL:hal-00656181v2
Volume: Volume 14 - 2011 - Special issue CARI'10
Published on: August 24, 2011
Submitted on: January 30, 2011
Keywords: Local and global stability,Bilharzia,Metapopulation model,Spatial heterogeneity,Strongly monotone systems,stabilité globale et locale,systèmes fortements monotones,Bilharziose,modèles de Métapopulations,hétérogénéités spatiales,[MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS]
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