Global Asymptotic Stability in a Delay Differential Equation Model for Mosquito Population Suppression

A bio-safe dengue control strategy is to use Wolbachia,which can induce incomplete cytoplasmic incompatibility(CI)and reduce the mating competitiveness of infected males.In this work,we formulate a delay differential equation model,including both the larval and adult stages of wild mosquitoes,to assess the impacts of CI intensityξand mating competitivenessθof infected males on the suppression efficiency.Our analysis identifies a CI intensity thresholdξ*below which a successful suppression is impossible.Whenξ≥ξ*,the wild population will be eliminated ultimately if the releasing level exceeds the release amount threshold R*uniformly.The dependence of R*onξandθ,and the impact of temperature on suppression are further exhibited through numerical examples.Our analyses indicate that a slight reduction ofξis more devastating than significantly decrease ofθin the suppression efficiency.To suppress more than 95%wild mosquitoes during the peak season of dengue in Guangzhou,the optimal starting date for releasing is sensitive toξbut almost independent ofθ.One percent reduction ofξfrom 1 requires at least one week earlier in the optimal releasing starting date from 7 weeks ahead of the peak season of dengue.