The impact of predators of mosquito larvae on Wolbachia spreading dynamics

Dengue fever creates more than 390 million cases worldwide yearly. The most effective way to deal with this mosquito-borne disease is to control the vectors. In this work we consider two weapons, the endosymbiotic bacteria Wolbachia and predators of mosquito larvae, for combating the disease. As Wolbachia-infected mosquitoes are less able to transmit dengue virus, releasing infected mosquitoes to invade wild mosquito populations helps to reduce dengue transmission. Besides this measure, the introduction of predators of mosquito larvae can control mosquito population. To evaluate the impact of the predators on Wolbachia spreading dynamics, we develop a stage-structured five-dimensional model, which links the predator-prey dynamics with the Wolbachia spreading. By comparatively analysing the dynamics of the models without and with predators, we observe that the introduction of the predators augments the number of coexistence equilibria and impedes Wolbachia spreading. Some numerical simulations are presented to support and expand our theoretical results.