Wolbachia Dynamics in Mosquitoes with Incomplete CI and Imperfect Maternal Transmission by a DDE System

In this paper, we propose a delay differential equation model to describe the Wolbachia infection dynamics in mosquitoes in which the key factor of cytoplasmic incompactibility (CI) is incorporated in a more natural way than those in the literature. By analyzing the dynamics of the model, we are able to obtain some information on the impact of four important parameters: the competition capabilities of the wild mosquitoes and infected mosquitoes, the maternal transmission level and the CI level. The analytic results show that there are ranges of parameters that support competition exclusion principle, and there are also ranges of parameters that allow co-persistence for both wild and infected mosquitoes. These ranges account for the scenarios of failure of invasion, invasion and suppressing the wild mosquitoes, and invasion and replacing the wild mosquitoes. We also discuss some possible future problems both in mathematics and in modeling.