An impulsive model for Wolbachia infection control of mosquito-borne diseases with general birth and death rate functions

Mosquito-borne diseases are global health problems, which mainly affect low-income populations in tropics and subtropics. In order to prevent the transmission of mosquito-borne diseases, the intracellular symbiotic bacteria named as Wolbachia is becoming a promising candidate to interrupt the virus transmission. In this paper, an impulsive mosquito population model with general birth and death rate functions is established to study the cytoplasmic incompatibility (CI) effect caused by mating of Wolbachia-infected males and uninfected females. The dynamics of the spread of Wolbachia in mosquito population are studied, and the strategies of mosquito extinction or replacing Wolbachia-uninfected mosquitoes with Wolbachia-infected mosquitoes are analyzed. Moreover, the results are applied to models with specific birth and death rate functions. It is shown that strategies may be different due to different birth and death rate functions, the type of Wolbachia strains and the initial number of Wolbachia-infected mosquitoes. Furthermore, numerical simulations are conducted to illustrate our conclusions.