Dynamical behavior of a mosquito population suppression model composed of two sub-models

In this paper, a new mosquito population suppression model with stage and sex structure is constructed, which is composed of two sub-models switching each other. Sterile mosquitoes are released with period [Formula: see text] and remain sexually active for time [Formula: see text]. For the case [Formula: see text], three thresholds [Formula: see text] [Formula: see text] and [Formula: see text] are determined for the release period [Formula: see text] and release amount [Formula: see text]. According to the values of [Formula: see text] and [Formula: see text] in different ranges determined by these thresholds, we study the dynamical behavior of the system for different release strategies, mainly including the existence and stability of the mosquito-extinction equilibrium and positive periodic solutions. Finally, some numerical simulations are performed to illustrate our results.