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Multiple endemic equilibria for the multipatch Ross-Macdonald with fast migrations

Abstract : We study the extension of the classical Ross-Macdonald model which describes the dynamics of malaria, to heterogeneous environments composed of several geographics zones. We assume that the hosts migrate between zones while mosquitoes do not. The particular case where the rate of migration does not depend on the epidemiological status was completely studied in [1]. Here we are interested in the case where the migration rates vary with the epidemiological compartments. Assuming that migrations are fast compared to the speed of the epidemiological phenomenon, we use the aggregation method ( see [7] ) to reduce the model and give an explicit formula for the basic reproduction ratio R0. We show using numerical simulations that if R0 < 1, then the disease free equilibrium (DFE), is globally stable. When R0 > 1, we show that the model has multiple endemic equilibria.
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https://hal.inria.fr/hal-00764638
Contributor : Gauthier Sallet <>
Submitted on : Thursday, December 13, 2012 - 11:47:06 AM
Last modification on : Tuesday, March 2, 2021 - 5:12:05 PM

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  • HAL Id : hal-00764638, version 1

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Pierre Auger, Gauthier Sallet, Maurice Tchuente, Berge Tsanou. Multiple endemic equilibria for the multipatch Ross-Macdonald with fast migrations. 10th African Conference on Research in Computer Science and Applied Mathematics, 2010, Yamoussoukro, Côte d’Ivoire. pp.117-124. ⟨hal-00764638⟩

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