Multi-compartment models

Abstract : We consider models with a general structure which, for example, encompasses the so-called DI, SP or DISP models with mass action incidence. We give a very simple formule for the basic reproduction ratio R0. If R0 \leq 1, we prove that the disease free equilibrium is globally asymptotically stable on the nonnegative orthant. If R0 > 1, we prove the existence of a unique endemic equilibrium in the positive orthant and give an explicit formula. We prove the global asymptotic stability of the endemic equilibrium, when R0 > 1 for SP model.
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Discrete and Continuous Dynamical Systems - Series S, American Institute of Mathematical Sciences, 2007, Dynamical Systems and Differential Equations. Proceedings of the 6th AIMS International Conference., 2007 (Special), pp.506-519. 〈http://aimsciences.org/journals/displayArticles.jsp?paperID=2858〉
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Abderrahman Iggidr, Joseph Mbang, Gauthier Sallet, Jean-Jules Tewa. Multi-compartment models. Discrete and Continuous Dynamical Systems - Series S, American Institute of Mathematical Sciences, 2007, Dynamical Systems and Differential Equations. Proceedings of the 6th AIMS International Conference., 2007 (Special), pp.506-519. 〈http://aimsciences.org/journals/displayArticles.jsp?paperID=2858〉. 〈inria-00591683〉

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