Mosquito control models based on <i>Wolbachia</i> or sterile insect techniques

Wolbachia-based mosquito control strategy and the sterile insect technique are two prominent approaches for mosquito control. In this paper, by considering wild mosquito population consisting of Wolbachia-infected mosquitoes and uninfected mosquitoes, we formulate two mathematical models to explore feasible releasing strategies for suppressing or replacing wild Wolbachia-uninfected mosquitoes. Specifically, we analyze the frequency and quantity of releases required to either drive the wild mosquito population to extinction or achieve complete replacement by Wolbachia-infected mosquitoes. We identify several critical thresholds related to release size and waiting periods, which enable us to establish necessary and sufficient conditions for the existence and uniqueness of semi-trivial periodic solutions. Furthermore, we derive global stability results that provide valuable insights into the design of effective mosquito control strategies, contributing to the control of mosquito-borne infectious diseases.