Global asymptotic stability in a delay stage structured model for mosquito population suppression

A promising avenue to control mosquito-borne diseases such as dengue, malaria, and Zika involves releasing male mosquitoes carrying the bacterium Wolbachia in wild areas to drive female sterility by a mechanism called cytoplasmic incompatibility (CI). In this work, we initiate a preliminary assessment of how the combined impact of dispersal, incomplete CI and mating competitiveness on mosquito population suppression by a delay differential equation model. Our theoretical analyses indicate that the immigration of eggs plays a significant role in the suppression dynamics. For the case without egg immigration, we identify a threshold dispersal rate v* of adult mosquitoes, threshold CI density xi*, and threshold release ratio r*. A successful mosquito suppression would be established only when v < v*, xi > xi*, and r(t) >= r* uniformly. The immigration of eggs causes the threshold dynamics to be invalid, and warns an absolute failure of population suppression. The monotonicity of the adult steady-state in the dispersal rate and CI intensity indicates that choosing a suitable Wolbachia strain with strong CI intensity, or bringing down the dispersal rate of mosquitoes by blocking the suppression zones is a feasible strategy to obtain a better suppression level.