Mathematical modeling and analysis of the effect of optimal control of sustainable malaria interventions using Wolbachia and eco-friendly strategies in endemic regions for policy design

Abstract

In this study, a mathematical model, MSEIRS-LSEI, was formulated and analysed to assess the impact of environmentally responsible malaria control strategies in Burundi. Human and mosquito populations were divided into several epidemiological compartments to better understand transmission dynamics. Using the next-generation matrix method, the basic reproduction number (\(\mathcal{R}_{0}\)) was calculated, revealing a value of 2.046 in the absence of control measures, confirming the endemic nature of the disease in the region. Pontryagin’s maximum principle is applied to characterize optimal control strategies, including medical treatments, larval control, and the introduction of mosquitoes infected with the Wolbachia bacterium. Stability analyses show that the epidemic can be locally eradicated if \(\mathcal{R}_0\) is less than 1. Numerical simulations based on real-world data demonstrate that these interventions can significantly reduce, or even eliminate, infected human and vector populations. The study recommends the large-scale deployment of these measures and the future integration of vaccination to provide long-term protection for vulnerable populations.