Auger Pierre, Kouokam Etienne, Sallet Gauthier, Tchuente Maurice, Tsanou B. (2008). The Ross-Macdonald model in a patchy environment. Mathematical Biosciences, 216 (2), p. 123-131. ISSN 0025-5564.
Auger Pierre, Kouokam Etienne, Sallet Gauthier, Tchuente Maurice, Tsanou B.
Source
Mathematical Biosciences, 2008,
216 (2), p. 123-131 ISSN 0025-5564
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.
Plan de classement
Sciences fondamentales / Techniques d'analyse et de recherche [020]
;
Entomologie médicale / Parasitologie / Virologie [052]
