Mathematical modeling of malaria transmission global dynamics: taking into account the immature stages of the vectors

International audience In this paper we present a mathematical model of malaria transmission. The model isan autonomous system, constructed by considering two models: a model of vectorpopulation and a model of virus transmission. The threshold dynamics of each modelis determined and a relation between them established. Furthermore, the Lyapunovprinciple is applied to study the stability of equilibrium points. The common basicreproduction number has been determined using the next generation matrix and itsimplication for malaria management analyzed. Hence, we show that if the thresholddynamics quantities are less than unity, the mosquitoes population disappearsleading to malaria disappearance; but if they are greater than unity, mosquitoespopulation persists and malaria also. Finally, numerical simulations are carried out to support our mathematical result