Periodic Solutions for a Mosquito Population Suppression Model Based on Incomplete Cytoplasmic Incompatibility

We discuss the periodic dynamics of a periodic switching mosquito population suppression model including the existence of periodic solutions and the stability analysis of the origin and each periodic solution. Under the assumption that the waiting period T between two consecutive releases of Wolbachia-infected males is equal to or less than the waiting release period threshold T∗, we give sufficient conditions for the model to have a unique or exactly two periodic solutions, respectively. Our results provide an important complement to the study of periodic solutions in the references. Some numerical examples are provided to illustrate the validity of our theoretical results.