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 $\overline{T}$. We investigate the dynamical behavior of the system when the release period $T$ is shorter than the sexual lifespan $\overline{T}$, corresponding to a relatively frequent release. We first determine two important thresholds, $m_1^{\ast }$ and $m_2^{\ast }$, 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 $0<m<m_1^{\ast }$ and $m_1^{\ast }\le m<m_2^{\ast }$. Furthermore, by applying the comparison theorem of monotone systems, we demonstrate that the extinction equilibrium is globally asymptotically stable when $m\ge m_2^{\ast }$. Finally, numerical examples are presented to confirm our theoretical results.