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 sexually active for time $ \bar{T} $. We investigate the dynamical behavior of the system when the release period $ T $ is shorter than the sexual lifespan $ \bar{T} $, 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^*\leq m < m_2^* $. Furthermore, by applying the comparison theorem of monotone systems, we demonstrate that the extinction equilibrium is globally asymptotically stable when $ m\geq m_2^* $. Finally, numerical examples are presented to confirm our theoretical results.