A reaction-diffusion-advection model for Aedes aegypti mosquitoes in a time-periodic environment

Abstract

In this paper we consider a reaction–diffusion–advection model in a heterogeneous time-periodic environment to understand the dynamical behaviors of the Aedes aegypti mosquitoes, which are divided into two sub-populations: the winged form and an aquatic population. The left and right free boundaries are utilized to represent the expanding fronts of the habitat. The spatial–temporal threshold R0F(t) depending on spatial heterogeneity, temporal-periodicity, spatial diffusion and advection is introduced and investigated. Sufficient conditions for the vanishing or spreading of the mosquitoes are given and the long-time dynamical behavior of the solution when spreading occurs is discussed. Our analytical results show that small rate of oviposition and big mortality rates tend to enhance the eradication of the Aedes aegypti mosquitoes.