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Analysis of the dynamics of a class of models for vector-borne diseases with host circulation

Abstract : In this work we study the dynamics of a vector borne disease on a metapopulation model that accounts for host circulation. For such models, the movement network topology gives rise to a contact network topology, corresponding to a bipartite graph. Under the assumption that the contact network is strongly connected, we can define the basic reproductive number R_0 and show that this system has only two equilibria: the so called disease free equilibrium (DFE); and a unique interior equilibrium that exists if, and only if, the basic reproduction number, R_0, is greater that unity. We are also able to show that the DFE is globally asymptotically stable, if R_0 ≤ 1. If R_0 > 1, the dynamics is uniformly persistent and, with further assumptions on the contact network structure, we also show that the endemic equilibrium (EE) is globally asymptotically stable.
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https://hal.inria.fr/hal-00905926
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Submitted on : Monday, November 18, 2013 - 9:35:17 PM
Last modification on : Thursday, January 20, 2022 - 5:32:51 PM
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  • HAL Id : hal-00905926, version 1

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Abderrahman Iggidr, Gauthier Sallet, Max O. Souza. Analysis of the dynamics of a class of models for vector-borne diseases with host circulation. [Research Report] RR-8396, INRIA. 2013, pp.20. ⟨hal-00905926⟩

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