How Does the Enhanced Mortality of Wolbachia-Infected Immature Mosquitoes Affect Dengue Transmission?

Abstract

One of the promising strategies to reduce dengue transmission is to release Wolbachia-infected mosquitoes, which can reduce the reproductive success of wild female mosquitoes. We develop a dengue transmission model coupled with the Wolbachia infection to consider the impact of the increased mortality of Wolbachia-infected immature mosquitoes on Wolbachia invasion and dengue transmission. To begin with, we analyze the infection model of Wolbachia without dengue transmission dynamics. Next, we establish an optimal control model by introducing a control variable to simulate the continuous (daily) releases of Wolbachia-infected male mosquitoes and find the optimal control by using Pontryagin’s Maximum Principle. We determine the optimal release strategy by minimizing the total cost of releasing infected male mosquitoes. Then, the full dengue transmission model is analyzed. The basic reproduction number of dengue transmission is calculated using the next-generation matrix method. The stability of the dengue-free equilibrium is proved by using the method of monotone dynamical systems. Furthermore, we carry out sensitivity analysis to study the barrier effect of Wolbachia and the impact of the increased mortality of immature mosquitoes on dengue transmission. Our results suggest that the increased mortality of immature Wolbachia-infected mosquitoes is not conducive to Wolbachia establishment and dengue control, which also induces more Wolbachia-infected mosquitoes to be released. In particular, we estimate the threshold mortality rate of infected larvae by using bifurcation analysis, which provides a quantitative basis and theoretical support for rational selection of Wolbachia strains and scientific and effective practice of dengue control.