Modeling Wolbachia infection frequency in mosquito populations via a continuous periodic switching model

In this article, we develop a continuous periodic switching model depicting Wolbachia infection frequency dynamics in mosquito populations by releasing Wolbachia-infected mosquitoes, which is different from the discrete modeling efforts in the literature. We obtain sufficient conditions on the existence of a unique and exactly two periodic solutions and analyze the stability of each periodic solution, respectively. We also provide a brief discussion and several numerical examples to illustrate our theoretical results.