Influence of the competition in the spatial dynamics of a population of Aedes mosquitoes

In this article, we investigate a competitive reaction-diffusion system modelling the interaction between several species of mosquitoes. In particular, it has been observed that in tropical regions, Aedes aegypti mosquitoes are well established in urban area whereas Aedes albopictus mosquitoes spread widely in forest region. The aim of this paper is to propose a simple mathematical system modeling this segregation phenomenon. Moreprecisely, after modeling the dynamics by a competitive reaction-diffusion system with spatial heterogeneity, we prove that when there is a strong competition between these two species of mosquitoes, solutions to this system converge in long time to segregated stationary solutions. Then we study the influence of this strong competition on the success of a population replacement strategy using Wolbachia bacteria. Our theoretical results are also illustrated by some numerical simulations.