Public Health Interventions for Fractional Optimal Control of Buruli Ulcer

Buruli Ulcer, a devastating skin disease caused by Mycobacterium Ulcerans, poses considerable public health challenges in endemic areas. This article focuses on the use of fractional optimal control theory to prevent the spread of Buruli ulcers via integrated public health interventions. We formulated a mathematical model using the Atangana-Baleanu-Caputo fractional order derivative operator. We investigated the models existence and uniqueness and presented numerical simulations using the predict-evaluate-correct-evaluate (PECE) method of Adam-Bashforth Moulton. We also study the fractional optimal control problem (FOCP) to minimize the spread of the disease in the endemic regions. We employ the Fractional Pontryagins Maximum Principle (FPMP) and implement the forward-backward method to determine the extremals of the problem. Four control strategies were implemented: promoting health education on the use of protective clothing, enhancing vaccination rates, improving treatment protocols for infected individuals, and spraying insecticides to reduce water-bug populations. After examining the optimal control dynamics of the Buruli ulcer transmission model via multiple simulations with and without control, we discover that there is a substantial decrease in the population of infected humans and the water-bug population. Hence we conclude that the best strategy to implement is by applying all the control strategies suggested.