Periodic dynamics of a discrete mosquito population suppression model

In this paper, we formulate a discrete model to investigate the interactive dynamics of wild and sterile mosquitoes. A key modelling assumption is that sterile mosquitoes are released via an impulsive and periodic release strategy to achieve effective population suppression. We obtain a critical release ratio threshold c∗ that fully determines the dynamical behaviours of the model. Sufficient conditions for the existence of positive T-periodic solutions are derived. Stability analysis shows that the model exhibits bistable dynamics when two positive T-periodic solutions exist, semi-stable dynamics in the case of a unique positive T-periodic solution, and global stable dynamics in the absence of positive T-periodic solutions.