title: Multiscale analysis for a vector-borne epidemic model.
abstract: Traditional studies about disease dynamics have focused on global stability issues, due to their epidemiological importance. We study a classical SIR-SI model for arboviruses in two different directions: we begin by describing an alternative proof of previously known global stability results by using only a Lyapunov approach. In the sequel, we take a different view and we argue that vectors and hosts can have very distinctive intrinsic time-scales, and that such distinctiveness extends to the disease dynamics. Under these hypothesis, we show that two asymptotic regimes naturally appear: the fast host dynamics and the fast vector dynamics. The former regime yields, at leading order, a SIR model for the hosts, but with a rational incidence rate. In this case, the vector disappears from the model, and the dynamics is similar to a directly contagious disease. The latter yields a SI model for the vectors, with the hosts disappearing from the model. Numerical results show the performance of the approximation, and a rigorous proof validates the reduced models.
authors.affiliation: Departamento de Matemática Aplicada, Universidade Federal Fluminense, R. Mário Santos Braga, s/n, Niterói, RJ, 22240-920, Brazil, msouza@mat.uff.br.
authors.forename: Max O
authors.initials: MO
authors.lastname: Souza
mesh_terms: D000818:Animals; D001102:Arbovirus Infections / Q000453:epidemiology / Q000635:transmission / Q000821:virology*; D001103:Arboviruses / Q000254:growth & development*; D001179:Arthropod Vectors / Q000821:virology*; D003198:Computer Simulation; D058872:Epidemics; D054884:Host-Pathogen Interactions; D006801:Humans; D008954:Models, Biological
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