Revista de Saúde Pública
On-line version ISSN 1518-8787
OLIVA, W. M. and SALLUM, E. M.. Periodic dynamic systems for infected hosts and mosquitoes. Rev. Saúde Pública [online]. 1996, vol.30, n.3, pp. 218-223. ISSN 1518-8787. http://dx.doi.org/10.1590/S0034-89101996000300003.
A mathematical model for the purpose of analysing the dynamic of the populations of infected hosts anf infected mosquitoes when the populations of mosquitoes are periodic in time is here presented. By the computation of a parameter l (the spectral radius of a certain monodromy matrix) one can state that either the infection peters out naturally) (l £ 1) or if l > 1 the infection becomes endemic. The model generalizes previous models for malaria by considering the case of periodic coefficients; it is also a variation of that for gonorrhea. The main motivation for the consideration of this present model was the recent studies on mosquitoes at an experimental rice irrigation system, in the South-Eastern region of Brazil.
Keywords : Malaria [epidemiology]; Culicidae; Population dinamics; Ecology, vectors.