Modeling the dynamics of onchocerciasis using the Atangana–Baleanu fractional order with control measures

This study presents a fractional-order model using the Atangana–Baleanu–Caputo (ABC) derivative to analyze the spread and control of onchocerciasis. The model captures the memory effects inherent in the disease’s progression and includes human and vector populations. We explore the qualitative behavior of the system, including positivity, boundedness, and stability of equilibria. The basic reproduction number, R0 is derived using the next-generation matrix method, and sensitivity analysis identifies key parameters driving transmission. Optimal control strategies such as treatment, vector control, and education are evaluated using Pontryagin’s Maximum Principle. Numerical simulations using the Toufik–Atangana scheme show that combining treatment with vector control significantly reduces disease burden. The findings offer practical insights for designing more effective onchocerciasis control programs, especially in endemic regions.