Profiling the source of the dynamical complexity of a class of periodic switching mosquito population suppression models

In recent decades, the sterile insect technique (SIT) and incompatible insect technique (IIT) have emerged as promising strategies for suppressing mosquitoes and controlling mosquito-borne diseases. To optimize these approaches and design cost-effective release strategies, mathematical models incorporating periodic switching and density-dependent survival probabilities have been developed to explore mosquito population dynamics. These models often exhibit rich and intricate behaviors. In this study, we introduce a periodically switched mosquito population suppression model that employs the Beverton–Holt-type survival probability, replacing the classic Ricker-type survival probability that increases the complexity of model dynamics. Through theoretical analyses and numerical simulations, we identify that the dynamical complexity observed in such models primarily stems from the interactions between wild and sterile mosquitoes, rather than the specific form of the survival probability. To the best of our knowledge, this study is the first to disentangle the dynamical complexity mechanisms in mosquito population models. These findings not only advance our understanding of density-dependent regulation but also provide actionable insights for optimizing SIT-based control strategies to achieve cost-efficient vector suppression.