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

Abstract

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, (Formula presented.), 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 (Formula presented.). For (Formula presented.), 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.