Global dynamics of a mosquito population suppression model with stage and sex structure

In this paper, we study a kind of mosquito population suppression model incorporating the growth stage as well as the sex structure of mosquitoes. For the general non-autonomous case, a threshold $m^{\ast }$ for the number of sexually active sterile mosquitoes in the field is defined, and sufficient conditions for successful suppression and partial suppression of wild mosquito population are obtained. For the first special case when the release period of the sterile mosquito is equal to its sexual lifespan, we determined the initial population size under which the mosquito population can be suppressed finally for different release intensities. For the latter special case when sterile mosquitoes are released with a constant rate, we give a threshold $u^{\ast }$ for the release rate, and investigate the dynamic behavior of the system based on this threshold. Finally, some numerical examples are presented to confirm the theoretical results.