A malaria transmission model with seasonal mosquito life-history traits

In this paper we develop and analyse a malaria model with seasonality of mosquito life-history traits: periodic-mosquitoes per capita birth rate, -mosquitoes death rate, -probability of mosquito to human disease transmission, -probability of human to mosquito disease transmission and -mosquitoes biting rate. All these parameters are assumed to be time dependent leading to a nonautonomous differential equation systems. We provide a global analysis of the model depending on two thresholds parameters [Formula] and [Formula] (with [Formula]). When [Formula], then the disease-free stationary state is locally asymptotically stable. In the presence of the human disease-induced mortality, the global stability of the disease-free stationary state is guarantied when [Formula]. On the contrary, if [Formula], the disease persists in the host population in the long term and the model admits at least one positive periodic solution. Moreover, by a numerical simulation, we show that a subcritical (backward) bifurcation is possible at [Formula]. Finally, the simulation results are in accordance with the seasonal variation of the reported cases of a malaria-epidemic region in Mpumalanga province in South Africa.