The impact of mating competitiveness and incomplete cytoplasmic incompatibility on Wolbachia-driven mosquito population suppression

To control mosquito-borne diseases such as dengue, malaria, and Zika, Wolbachia-infected male mosquitoes have been released in open areas to suppress wild mosquito population driven by cytoplasmic incompatibility (CI). In this work, we initiate a preliminary assessment on how the CI intensity xi, and the mating competitiveness mu of released males relative to wild males, impact the suppression efficacy by a delay differential equation model. Our analysis identifies a threshold CI intensity xi(0) is an element of (0, 1) as an increasing function of the natural reproduction rate of the wild mosquitoes, and a threshold value r* for the ratio r(t) between the numbers of released males and wild males. The population suppression fails when xi <= xi(0), and succeeds when xi > xi(0) and r(t) >= r*. Our analyses indicate that xi plays a more important role than mu in the population suppression. For instance, a slight decrease of xi from 1 to 0.92 is more devastating than halving mu from 1 to 0.5. In our estimation of the optimal starting date for infected male release to target a more than 95% wild population reduction during the peak season of dengue in Guangzhou, we find that the optimal date is almost independent of mu but is sensitive to xi. If CI is complete, then starting about two months ahead can be an optimal option for less financial and labor costs. A slight reduction in the CI intensity requires a considerably earlier starting date.