A malaria transmission model with seasonal mosquito life-history traits

Abstract

AbstractIn 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 parametersand(with). When, 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. On the contrary, if, 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. 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.