Sustained oscillatory mosquito population suppression analysis based on a hybrid switching dynamical system model

In this paper, we develop a hybrid dynamical system to model mosquito population suppression incorporating both time and state-dependent switching. The time-dependent switching arises from a mismatch between the sexual lifespan of sterile mosquitoes and the sampling period, while the state-dependent switching is governed by the relation between the state of wild mosquitoes at sampling instants and the epidemiological threshold. We investigate the long-term dynamics of the hybrid system with sampling period exceeding the sexual lifespan. The wild population is shown to converge to a pseudo-equilibrium when the epidemiological threshold exceeds this equilibrium value. For the other situation, we establish sufficient conditions for the existence of a unique (pseudo)-harmonic solution and analyze its stability. Using Poincaré mapping, we further derive explicit existence criteria for subharmonic solutions and rigorously prove their global asymptotic stability. Finally, some numerical examples are provided to illustrate our theoretical findings and to deliver practical insights for release strategy development.