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

Authors

  • Danat Nanle Tanko
    School of Mathematical Sciences, Universiti Sains Malaysia, 11800 USM, Pulau Pinang, Malaysia
    Department of Mathematics, Plateau State University Bokkos, 2012 Jos, Plateau State, Nigeria
  • Farah Aini Abdullah
    School of Mathematical Sciences, Universiti Sains Malaysia, 11800 USM, Pulau Pinang, Malaysia
    https://orcid.org/0000-0002-5215-9617
  • Majid K. M Ali
    School of Mathematical Sciences, Universiti Sains Malaysia, 11800 USM, Pulau Pinang, Malaysia
  • Matthew O. Adewole
    School of Mathematical Sciences, Universiti Sains Malaysia, 11800 USM, Pulau Pinang, Malaysia.
    Department of Computer Science and Mathematics, Mountain Top University, Prayer City, Ogun State, Nigeria
  • James Andrawus
    Department of Mathematics, Federal University, Dutse 7156, Jigawa, Nigeria

Keywords:

Caputo-Fabrizio fractional derivative, Existence, Stability, Fractional Adams-Bashforth Numerical scheme, Onchocerciasis model

Abstract

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.

Dimensions

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Published

2026-02-01

How to Cite

Onchocerciasis control via Caputo-Fabrizio fractional dynamics: a focus on early treatment and vector management strategies. (2026). Journal of the Nigerian Society of Physical Sciences, 8(1), 2942. https://doi.org/10.46481/jnsps.2026.2942

Issue

Volume 8, Issue 1, February 2026

Section

Mathematics & Statistics
Copyright & Licensing

Copyright (c) 2025 Danat Nanle Tanko, Farah Aini Abdullah, Majid K. M Ali, Matthew O. Adewole, James Andrawus (Author)

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This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Onchocerciasis control via Caputo-Fabrizio fractional dynamics: a focus on early treatment and vector management strategies. (2026). Journal of the Nigerian Society of Physical Sciences, 8(1), 2942. https://doi.org/10.46481/jnsps.2026.2942

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