(untitled) (Journal of Nonlinear Modeling and Analysis, 2024)
Consider that infection with Wolbachiacan limit a mosquito's ability to transmit Dengue fever virus through its saliva, a mathematical model describing the transmission of Dengue fever between vector mosquitoes and human, incorporating Wolbachia-carrying mosquito population and seasonal fluctuation, is proposed. Firstly, the stability and bifurcation of this model are investigated exactly in the case where seasonality can be neglected. Further, the basic reproductive number R_0^s for this model with seasonal variation is obtained, that is, if R_0^s is less than unity the disease is extinct and R_0^s is greater than unity the disease is uniformly persistent. Finally, numerical simulations verify the theoretical results. Theoretical results suggest that, compared with the mosquito reduction strategies (such as the elimination of mosquito breeding sites, killing of adult mosquitoes by spraying), introducing Wolbachia strains is as effectual to fight against the transmission of Dengue virus.