Development and analysis of a malaria transmission mathematical model with seasonal mosquito life‐history traits

Abstract

In this paper, we develop and analyze 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 system. We provide a global analysis of the model depending on two threshold parameters 0 and 0 < 1 (with 0 ≤ 0). When 0 < 1, 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 0 < 1. On the contrary, if 0 > 1, 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 sub-critical (backward) bifurcation is possible at 0 = 1. 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.