GLOBAL DYNAMICS OF A MOSQUITO POPULATION SUPPRESSION MODEL UNDER A PERIODIC RELEASE STRATEGY

Abstract

It has been proved that periodic releases of <i>Wolbachia</i>-infected or irradiation-treated mosquitoes is an effective way to suppress wild mosquitoes and prevent the prevalence of mosquito-borne diseases. We have discussed some cases in consideration of the release amount $c$ and release period $T$, and in this paper we continue to explore the remaining complementary case and investigate the relevant stability of the origin and the exact number of periodic solutions in the switching model. Based on the release period threshold $T^*$ introduced in the extant works, we define a new threshold $T^{**}$ between the sexual lifespan $\bar{T}$ of sterile mosquitoes and $T^*$, and reveal the complete dynamics of the model, particularly, no $T$-periodic solutions when $T\in(\bar{T}, T^{**})$, a unique $T$-periodic solution when $T=T^{**}$, and exactly two $T$-periodic solutions when $T\in(T^{**}, T^*)$. Finally, we give some numerical simulations to seek the approximate value of $T^{**}$ and demonstrate the global dynamical behaviors of wild mosquito population.