Modeling incomplete sterility and immigration in mosquito suppression by delay differential equations

A promising avenue for the control of mosquito-borne diseases such as dengue fever, malaria and Zika is to sterilize female mosquitoes by releasing the males carrying the bacterium Wolbachia through a mechanism cytoplasmic incompatibility (CI). In this work, we develop a model of delay differential equations, incorporating larval and adult stages, to assess the delicate impact of the incomplete CI, weak mating competitiveness of infected males and immigration of wild mosquitoes from surrounding uncontrolled areas on suppression efficiency. Our analyses identify the thresholds of CI intensity and immigration number to ensure that the model displays globally asymptotically stable dynamics. We quantify the maximum suppression efficiency by the maximum relative reduction of wild adult mosquitoes, which increases almost linearly in the CI intensity and decreases almost linearly in the immigration number when it is no more than [Formula: see text] of the carrying capacity. To reduce [Formula: see text] of wild adult mosquitoes in the peak season within 7 weeks, we find that the least release number would be reduced effectively by increasing the CI intensity or decreasing the immigration number.