Modeling Mosquito Population Suppression Using Beverton–Holt Offspring Survival Probability

Abstract

In this paper, we develop a mathematical model for mosquito population suppression based on a Beverton–Holt type of offspring survival probability. We focus on the scenarios where sterile mosquitoes are released impulsively and periodically under the condition that the release period $T$ is either equal to or greater than the sexually active lifespan $\overline{T}$ of the sterile mosquitoes. For the case where $T=\overline{T}$, we rigorously analyze the existence and stability of equilibrium states. When $T>\overline{T}$, the model transforms into two switching equations. Our analysis demonstrates that in the absence of periodic solutions, the origin is globally asymptotically stable, whereas when a unique periodic solution exists, it is either globally asymptotically stable or semistable. In the scenarios where two periodic solutions emerge, one is stable and the other is unstable. Numerical simulations further illustrate the periodic dynamics of the model.