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Optimal Control Analysis of Onchocerciasis through Multiple Integrated Control Measures
  • Mohamedi S. Manjenga,
  • Joshua Mwasunda,
  • Jacob I. Irunde
Mohamedi S. Manjenga
Mkwawa University College of Education

Corresponding Author:[email protected]

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Joshua Mwasunda
Mkwawa University College of Education
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Jacob I. Irunde
Mkwawa University College of Education
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Abstract

Onchocerciasis also known as River Blindness, is a vector-borne disease caused by Onchocerca volvulus and transmitted by infected female blackflies. It affects millions of people globally, with the greatest impact in sub-Saharan Africa. In this study, we develop a deterministic mathematical model that integrates multiple control measures, including Sterile Insect Technique (SIT), mechanical control, chemical control, public health education and ivermectin treatment, to manage the transmission of onchocerciasis. We employ the next-generation matrix method to calculate the blackfly offspring reproduction number N 0 and the basic reproduction number R 0 . Sensitivity analysis, conducted using the normalized forward sensitivity index, highlights the biting rate as the most positive influence on driving onchocerciasis dynamics, while the mortality rate of female blackflies has a significant negative impact on disease containment. To identify the optimal control strategy, we apply optimal control theory, considering five time-dependent controls which are public health education, treatment, mechanical control, SIT and chemical control. Using Pontryagin’s maximum principle, we derive the optimality system for controlling onchocerciasis. By implementing forward-backward Runge-Kutta method in Matlab, we identify the most optimal strategy for controlling, preventing and treating onchocerciasis in both human and blackfly populations. The results suggest that a combined strategy focusing on public health education, treatment and SIT offers the most effective approach for combating onchocerciasis.
11 Oct 2024Submitted to Mathematical Methods in the Applied Sciences
14 Oct 2024Submission Checks Completed
14 Oct 2024Assigned to Editor
25 Oct 2024Review(s) Completed, Editorial Evaluation Pending
10 Nov 2024Reviewer(s) Assigned