Dynamical modeling and bifurcation analysis of malaria transmission under synergistic control of Wolbachia-infected male release and chemical insecticides.

In this article, we integrate the release of Wolbachia-carrying male mosquitoes with chemical insecticide spraying to formulate a coupled model that incorporates mosquito stage structure and malaria transmission dynamics. The model accounts for mating competition influenced by cytoplasmic incompatibility and employs a Holling-II type saturated release mechanism to dynamically match the release intensity of infected male mosquitoes with the density of wild mosquitoes. The study first verifies the positive invariance and boundedness of solutions of the model. It then derives the basic reproduction number, followed by the existence conditions and stability properties of equilibria. Subsequently, it reveals saddle-node bifurcation, forward bifurcation, backward bifurcation and their compound phenomena, thereby elucidating the abrupt dynamic changes near parameter thresholds of the system. Numerical simulations validate the theoretical results, quantify the regulatory effects of key parameters, and confirm that the combined strategy effectively suppresses mosquito population growth and interrupts malaria transmission through synergistic effects. The results illustrate that accurate tuning of critical parameters for the integrated control strategy and exploitation of synergism between Wolbachia and chemical insecticides can effectively modulate mosquito populations and block malaria transmission.