Investigating Malaria Spread and Optimal Control Measures with Prompt and Delayed Treatments
DOI:
https://doi.org/10.70882/josrar.2025.v2i3.89Keywords:
Center manifold analysis, Dynamic stability, Intervention strategies, Malaria, Mosquito management, Optimal control, Timely treatmentAbstract
Malaria, transmitted by Anopheles mosquitoes carrying Plasmodium parasites, poses a significant health burden, especially in tropical regions. This study employs a mathematical framework to explore malaria dynamics, emphasizing system stability and effective interventions that incorporate immediate (IEh) and delayed (ILh)treatment strategies. Using center manifold analysis, we investigate stability at the critical threshold R0=1, identifying a forward bifurcation (a<0, b>0), indicating that maintaining R0 below 1 halts disease persistence. By applying Pontryagin’s principle and numerical optimization techniques, we formulate control strategies integrating rapid treatment, mosquito population management, and reduction of untreated infections, achieving a controlled reproduction number of Rc0=0.1964, compared to an uncontrolled R0=2.2356. These findings underscore the efficacy of combined interventions and provide actionable insights for malaria control in resource-limited settings.
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