Global dynamics of a mosquito population suppression model with seasonal switching

Abstract

In this paper, we establish and analyze a mosquito population suppression model with seasonal switching. Under the assumption that the ratio of sexually active Wolbachia-infected males and wild mosquitoes is kept at a constant level during the favorable seasons, we give a rather complete description on the dynamics including the stability of the origin, existence, stability and semi-stability of a unique, exact two periodic solutions, and so on. We obtain sufficient conditions for the origin to be globally asymptotically stable, for the model to have a unique semi-stable periodic solution, and to have exactly two periodic solutions among which one is stable and the other is unstable, respectively. Numerical examples to support our theoretical results and brief discussions are also provided.