Modelling the Effects of Wolbachia-Carrying Male Augmentation and Mating Competition on the Control Of Dengue Fever

Dengue fever is the most common arboviral infection of humans, responsible for a substantial disease burden to the world. Lately, an innovative technology has been approved to suppress natural mosquitoes by releasing Wolbachia-carrying male mosquitoes. To depict the transmission of dengue virus among mosquito and human populations, we respectively couple a stage-structure mosquito population model with and without male augmentation and mating competition into a dengue epidemic model. Dynamical properties of the two high dimensional systems are investigated, including the invariance and boundedness, the existence and local stability of their equilibria and bifurcation analysis. It reveals that there may be a forward or backward bifurcation, or a combination of a saddle-node bifurcation and a forward or backward bifurcation. Moreover, global dynamical properties are explored by comprehensively using the properties of limit system, Lyapunov function and geometric approach. Our results suggest that male augmentation cannot always ensure the eradication of mosquitoes or dengue cases, but it can suppress dengue epidemic to a certain extent. Thus we define the five possible suppression levels of dengue fever and obtain their suppression rates. Also, we investigate how release ratio, mating competition, the rate of cytoplasmic incompatibility and the basic offspring number affect the suppression rates. Finally, under different environment situations, we discuss how to combine male releases, traditional mosquito control methods and human control measures to suppress dengue cases. This study will be helpful for public health authorities in designing proper strategies to control and prevent the epidemics of dengue fever.