Mathematical modeling of malaria transmission global dynamics: taking into account the release of Wolbachia-infected male mosquitoes

This article presents a mathematical model of malaria transmission dynamics that integrates the release of Wolbachia-infected male mosquitoes with mechanical control strategies and larvicide treatment. A key aspect of our analysis is the determination of the basic reproduction number, ${{\mathcal R}_0}$R0, which reveals a critical relationship with the number of Wolbachia-infected male mosquitoes released. We identified two equilibrium states: the disease-free equilibrium, where malaria is eradicated, and the endemic equilibrium, where the disease persists. By constructing a suitable Lyapunov function, we demonstrated the global asymptotic stability of the disease-free equilibrium when ${{\mathcal R}_0} \le 1$R0≤1. For ${{\mathcal R}_0} \gt 1$R0>1, we examined the local asymptotic stability of the endemic equilibrium. To illustrate our theoretical findings, we conducted numerical simulations across diverse scenarios. Our results highlight the potential of Wolbachia-infected male mosquitoes releases interventions to significantly impact malaria transmission, particularly when combined with mechanical control and larvicide treatment.