Stability and periodicity in a mosquito population suppression model composed of two sub-models.

In this paper, we propose a mosquito population suppression model which is composed of two sub-models switching each other. We assume that the releases of sterile mosquitoes are periodic and impulsive, only sexually active sterile mosquitoes play a role in the mosquito population suppression process, and the survival probability is density-dependent. For the release waiting period T and the release amount c, we find three thresholds denoted by T ∗ , g ∗ , and c ∗ with c ∗ > g ∗ . We show that the origin is a globally or locally asymptotically stable equilibrium when c ≥ c ∗ and T ≤ T ∗ , or c ∈ (g ∗ , c ∗) and T < T ∗ . We prove that the model generates a unique globally asymptotically stable T-periodic solution when either c ∈ (g ∗ , c ∗) and T = T ∗ , or c > g ∗ and T > T ∗ . Two numerical examples are provided to illustrate our theoretical results. [ABSTRACT FROM AUTHOR]