title: Malaria model with periodic mosquito birth and death rates.
abstract: In this paper, we introduce a model of malaria, a disease that involves a complex life cycle of parasites, requiring both human and mosquito hosts. The novelty of the model is the introduction of periodic coefficients into the system of one-dimensional equations, which account for the seasonal variations (wet and dry seasons) in the mosquito birth and death rates. We define a basic reproduction number R(0) that depends on the periodic coefficients and prove that if R(0)<1 then the disease becomes extinct, whereas if R(0)>1 then the disease is endemic and may even be periodic.
authors.affiliation: Department of Mathematics and Computer Science, Grambling State University, Grambling, LA, USA.
authors.forename: Bassidy
authors.initials: B
authors.lastname: Dembele
authors.forename: Avner
authors.initials: A
authors.lastname: Friedman
authors.forename: Abdul-Aziz
authors.initials: AA
authors.lastname: Yakubu
mesh_terms: D000818:Animals; D009033:Culicidae / Q000254:growth & development*; D004198:Disease Susceptibility; D019353:Endemic Diseases / Q000706:statistics & numerical data; D006801:Humans; D008018:Life Cycle Stages; D008288:Malaria / Q000453:epidemiology / Q000469:parasitology*; D008954:Models, Biological; D011157:Population Dynamics