title: A mathematical model for malaria involving differential susceptibility, exposedness and infectivity of human host.
abstract: The main purpose of this article is to formulate a deterministic mathematical model for the transmission of malaria that considers two host types in the human population. The first type is called "non-immune" comprising all humans who have never acquired immunity against malaria and the second type is called "semi-immune". Non-immune are divided into susceptible, exposed and infectious and semi-immune are divided into susceptible, exposed, infectious and immune. We obtain an explicit formula for the reproductive number, R(0) which is a function of the weight of the transmission semi-immune-mosquito-semi-immune, R(0a), and the weight of the transmission non-immune-mosquito-non-immune, R(0e). Then, we study the existence of endemic equilibria by using bifurcation analysis. We give a simple criterion when R(0) crosses one for forward and backward bifurcation. We explore the possibility of a control for malaria through a specific sub-group such as non-immune or semi-immune or mosquitoes.
authors.affiliation: INRIA-Anubis Sud-Ouest futurs, Université de Bordeaux, UFR Sciences et Modélisation, 146 rue Leo Saignat BP 26, Bordeaux Cedex, France. arnaud.ducrot@u-bordeaux2.fr
authors.forename: A
authors.initials: A
authors.lastname: Ducrot
authors.forename: S B
authors.initials: SB
authors.lastname: Sirima
authors.forename: B
authors.initials: B
authors.lastname: Somé
authors.forename: P
authors.initials: P
authors.lastname: Zongo
mesh_terms: D003198:Computer Simulation; D004198:Disease Susceptibility / Q000453:epidemiology* / Q000469:parasitology*; D019353:Endemic Diseases / Q000706:statistics & numerical data; D006801:Humans; D008288:Malaria / Q000517:prevention & control / Q000635:transmission*; D008954:Models, Biological; D010961:Plasmodium / Q000472:pathogenicity*