Modeling and analysis of release strategies of sterile mosquitoes incorporating stage and sex structure of wild ones

This paper proposes and studies a switched interactive model of wild and sterile mosquitoes with stage and sex structure. Sterile males are released periodically and impulsively and remain sexu-ally active for time T over bar . We investigate the dynamical behavior of the system when the release period T is shorter than the sexual lifespan T over bar , corresponding to a relatively frequent release. We first determine two important thresholds, m*1 and m*2, for the release amount m and prove the exponential asymptotic stability of the extinction equilibrium. Using fixed point theory, we establish the existence of positive periodic solutions for 0 < m < m*1 and m*1 <= m < m*2. Furthermore, by applying the comparison the-orem of monotone systems, we demonstrate that the extinction equilibrium is globally asymptotically stable when m >= m*2. Finally, numerical examples are presented to confirm our theoretical results.