对布里溃疡进行分段优化控制的公共卫生干预措施

Solomon Nortey, Ernest Akorly, Mark Dadzie, Stephen E. Moore
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摘要

布路里溃疡是一种由溃疡分枝杆菌引起的破坏性皮肤病,给流行地区的公共卫生带来了巨大挑战。本文重点探讨如何利用分数最优控制理论,通过综合公共卫生干预措施防止布路里溃疡的传播。我们利用 Atangana-Baleanu-Caputo 分数阶导数算子建立了一个数学模型。我们研究了该模型的存在性和唯一性,并使用 Adam-Bashforth Moulton 的预测-评估-纠正-评估(PECE)方法进行了数值模拟。我们还研究了分数最优控制问题(FOCP),以尽量减少疾病在流行地区的传播。我们采用了分数庞特里亚金最大原则(FPMP),并实施了前向-后向方法来确定问题的极值。我们实施了四种控制策略:推广使用防护服的健康教育、提高疫苗接种率、改进感染者的治疗方案以及喷洒杀虫剂以减少水虱数量。我们通过多次模拟研究了布路里溃疡传播模型的最佳控制动态,发现在有控制和无控制的情况下,受感染的人类数量和水虱数量都会大幅减少。因此,我们得出结论,实施的最佳策略是采用建议的所有控制策略。
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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 model’s 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 Pontryagin’s 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.
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