Onchocerciasis control via Caputo-Fabrizio fractional dynamics: a focus on early treatment and vector management strategies

The socio-economic burdens of onchocerciasis have prompted the formulation of several mathematical models to better comprehend the epidemic. However, existing models either use integer-order derivatives, which often do not capture the memory and non-local effects seen in infectious diseases, or fractional order with singularity kernels, which may inadequately represent memory effects due to their singularity kernels. Onchocerciasis has a prolonged incubation and slow progression, making past conditions impactful on the disease's current and future course. Fractional derivatives effectively capture this memory effect, providing a more realistic depiction of the infection dynamics than integer-order models. We propose a non-local, non-singular exponential kernel fractional-order onchocerciasis model in the Caputo-Fabrizio fractional derivative sense to capture the disease's memory effects. Our model incorporates early treatment of exposed individuals as a critical intervention parameter, and vector management strategies are also incorporated. Using fixed-point theorem and iterative methods, we establish the existence and uniqueness of solutions, derive conditions for onchocerciasis-free and endemic equilibrium points, and analyze their stability, confirming the model's biological feasibility. Numerical simulations are conducted using a three-step fractional Adams-Bashforth method. Sensitivity analyses indicate that vector management and early treatment effectively reduce the effective reproduction number, while increases in the human-to-vector contact rate elevate it. Numerical results demonstrate that early treatment and vector management can significantly control onchocerciasis. The fractional-order "memory effect" highlights the importance of continuous monitoring and consistent application of control measures to reduce the memory index and curb onchocerciasis prevalence over time.