The Ross–Macdonald model in a patchy environment

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• 作者：Pierre Auger ; Etienne Kouokam ; Gauthier Sallet ; Maurice Tchuente ; Berge Tsanou
• 关键词：Metapopulation models ; Vector-borne diseases ; Ross– ; Macdonald model ; Nonlinear dynamical systems ; Global stability ; Monotone systems
• 刊名：Mathematical Biosciences
• 出版年：2008
• 出版时间：December 2008
• 年：2008
• 卷：216
• 期：2
• 页码：123-131
• 全文大小：605 K

文摘

We generalize to n patches the Ross–Macdonald model which describes the dynamics of malaria. We incorporate in our model the fact that some patches can be vector free. We assume that the hosts can migrate between patches, but not the vectors. The susceptible and infectious individuals have the same dispersal rate. We compute the basic reproduction ratio . We prove that if , then the disease-free equilibrium is globally asymptotically stable. When , we prove that there exists a unique endemic equilibrium, which is globally asymptotically stable on the biological domain minus the disease-free equilibrium.