The invasive dynamics of Aedes aegypti mosquito in a heterogenous environment

Abstract

A reaction-diffusion-advection model is proposed and investigated to understand the invasive dynamics of Aedes aegypti mosquitoes. The free boundary is introduced to model the expanding front of the invasive mosquitoes in a heterogenous environment. The threshold $R_0^D$ for the model with Dirichlet boundary condition is defined and the threshold $R_0^F(t)$ for the free boundary problem is introduced, and the long-time behavior of positive solutions to the reaction-diffusion-advection system is discussed. Sufficient conditions for the mosquitoes to be eradicated or to spread are given. We show that, if $R_0^F(\infty )\le 1$, the mosquitoes always vanish, and if $R_0^F(t_0)\ge 1$ for some $t_0\ge 0$, the mosquitoes must spread, while if $R_0^F(0)<1<R_0^F(\infty )$, the spreading or vanishing of the mosquitoes depends on the initial number of mosquitoes, or mosquitoes' invasive ability on the free boundary.

25 pages