The impact of incomplete cytoplasmic incompatibility on mosquito population suppression by <i>Wolbachia</i>

Mosquito-borne diseases have become a serious threat to human health worldwide. As Wolbachia may induce cytoplasmic incompatibility (CI) and cause embryonic death when infected male mosquitoes mate with uninfected females, suppressing mosquito population by releasing infected male mosquitoes has become an effective strategy to prevent mosquito-borne diseases. In this paper, we build delay differential equations to study mosquito population suppression with constant releases of Wolbachia infected mosquitoes with incomplete CI. By discussing the existence of multiple equilibria and analyzing the global dynamics completely determined by the intensity threshold of CI and releasing thresholds, we confirm the possibility of bistable and semi-stable phenomena. Numerical simulations show that the intensity threshold $ s_h^* $ of CI combined with the releasing threshold $ r^* $ can help to select Wolbachia strains, and cut down the suppression duration by improving the intensity of CI. Sensitivity analysis shows that both the CI intensity and the time delay also have significant influence on the suppression duration. In addition, we illustrate how the releasing threshold $ r_1 $ and the suppression duration $ T $ change with different Wolbachia strains.