title: The Ross-Macdonald model in a patchy environment.
abstract: 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 R(0). We prove that if R(0)1, then the disease-free equilibrium is globally asymptotically stable. When R(0)>1, we prove that there exists a unique endemic equilibrium, which is globally asymptotically stable on the biological domain minus the disease-free equilibrium.
authors.affiliation: IRD, UR GEODES, 32 Avenue Henri Varagnat, 3143 Bondy Cedex, France.
authors.forename: Pierre
authors.initials: P
authors.lastname: Auger
authors.forename: Etienne
authors.initials: E
authors.lastname: Kouokam
authors.forename: Gauthier
authors.initials: G
authors.lastname: Sallet
authors.forename: Maurice
authors.initials: M
authors.lastname: Tchuente
authors.forename: Berge
authors.initials: B
authors.lastname: Tsanou
mesh_terms: D000818:Animals; D050936:Basic Reproduction Number; D003198:Computer Simulation; D009033:Culicidae / Q000469:parasitology*; D006801:Humans; D007303:Insect Vectors / Q000469:parasitology*; D008288:Malaria / Q000453:epidemiology / Q000635:transmission*; D008954:Models, Biological; D010961:Plasmodium / Q000254:growth & development*; D015995:Prevalence