Optimal Control Analysis of Onchocerciasis Through Multiple Integrated Control Measures

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 for onchocerciasis infections, 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 chemical control offers the most effective approach for combating onchocerciasis.