| Abstract: |
| Releasing {\it Wolbachia}-infected mosquitoes to control wild mosquitoes is a promising avenue. Many studies have been devoted to using mathematical tools to find the optimal control strategy. However, the impact of diffusion of uninfected/infected mosquitoes is less understood. To describe the discretization of release sites, a two-patch mosquito suppression model with time delay and impulsive release is investigated in this paper. Particularly, we assume that the waiting period between two consecutive releases is equal to the sexual lifespan of infected males. We confirm the well-posedness and monotonicity of the solution and explore the existence and stability of equilibria. For some parameter regimes, we give sufficient conditions for a bistable structure. Based on this, we establish the existence of the separatrix with some sharp estimates when choosing constant functions as initial values. More interestingly, the monotonicity of the separatrix in the release number is proved, implying the existence of an optimal release strategy. We also found that the higher the cytoplasmic incompatibility intensity, the more likely wild mosquitoes are suppressed, and releasing infected males at as many spots as possible is more effective. |
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