Bifurcations of an impulsive mosquito population model with Wolbachia control and insecticide spraying

As a mosquito-borne infectious disease, dengue fever poses a severe threat to human health. Female mosquitoes carrying Wolbachia can significantly inhibit dengue virus replication within them. Combining chemical insecticides with Wolbachia can effectively prevent the spread of dengue virus while reducing mosquito bites. In our previous work, a mosquito dynamical model with impulsive spraying insecticide was proposed to study Wolbachia spreading within the mosquito population via exploring its stability and persistence. Note that the occurrence of bifurcations of the system can impact the threshold conditions for mosquito control strategies. In this work, we further prove the existence of forward and backward bifurcations for the impulsive system. Numerical parameter bifurcation diagrams are presented to explore the impact of maternal inheritance rate and mosquito death rates on the periodic solutions and mosquito control. Moreover, the effects of initial mosquito density on bistable dynamical behaviors are examined by the basin of attraction of periodic solutions. The results indicate that compared to only Wolbachia biology control, the integrated control strategy can not only effectively reduce, even eradicate mosquitoes, but also help to increase parameter ranges for the success of mosquito replacement. This work provides valuable insights for designing integrated mosquito control to restrain the spread of dengue diseases.