Modeling of periodic compensation policy for sterile mosquitoes incorporating sexual lifespan

In this paper, a delayed mosquito population suppression model with stage and sex structure is constructed incorporating periodic releases of the sterile mosquito and its sexual lifespan. Sterile mosquitoes are released periodically into the field to suppress the wild mosquito population, and only sexually active sterile mosquitoes are included in the interaction system of these two populations. According to the relationship between the release period T$$ T $$ and the sexual lifespan T1$$ {T}_1 $$, we study the dynamic behaviors of the system, such as the existence of positive periodic solutions and the stability of extinction equilibrium in three cases. A series of numerical simulations are performed, which not only verify the reliability of the theoretical results but also make a numerical analysis of the open problems raised in the theoretical research.