Analyzing the control of dengue by releasing Wolbachia -infected male mosquitoes through a delay differential equation model

To date, an innovative strategy to control dengue is to release Wolbachia -infected male mosquitoes into wild areas to sterilize wild female mosquito vectors by cytoplasmic incompatibility (CI). To investigate the efficacy of Wolbachia in blocking dengue virus transmission, we develop a deterministic mathematical model of human and mosquito populations in which one dengue serotype circulates. The delay differential equation model captures the respective extrinsic and intrinsic incu-bation periods (EIP and IIP) in the mosquito and human, as well as the maturation delay between mating and emergence of adult mosquitoes, which have received relatively little attention. We analyze the existence and stability of disease-free equilibria, and obtain a sufficient and necessary condition on the existence of the disease-endemic equilibrium. We also determine two threshold values of the release ratio $\theta$, denoted by $\theta_1^*$ and $\theta_2^*$ with $\theta_1^*>\theta_2^*$. When $\theta>\theta_1^*$, the mosquito population will be eradicated eventually. When $\theta_2^* Wolbachia in reducing dengue at a population level.