霍乱动态治疗策略的最优控制分析

IF 1 Q3 ENGINEERING, MULTIDISCIPLINARY
Sani Fakai Abubakar, M. Ibrahim
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引用次数: 2

摘要

建立了一个九室确定性霍乱模型,该模型描述了人类、霍乱弧菌细菌和保证相互作用的环境之间的相互作用。现实和社会经济负担影响疾病的传播和控制机制。该模型探讨了阻止霍乱爆发和传播的有效途径。确定了模型所包含的方程组解的存在唯一性。采用“下一代矩阵”法获得模型的基本再现数r0,采用“归一化前向灵敏度指数”法识别最敏感参数。选取卫生意识X1、霍乱疫苗X2和霍乱宣传规划X3 3个对照。应用最优控制理论确定了控制措施在减少易感、暴露、感染个体和致病病原体种群方面的效果水平。利用庞特里亚金极大值原理证明了模型的最优解,导出了最优系统并进行了数值求解。模拟用图表显示了控制对易感、暴露、感染和霍乱弧菌群体的影响。研究结果表明,同时应用这三种控制方法可能是控制霍乱的快速有效方法之一。如果选择两种对照,卫生意识和疫苗是最好的组合。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Optimal Control Analysis of Treatment Strategies of the Dynamics of Cholera
A nine-compartment deterministic cholera model was formulated, and the model describes interactions between human, Vibrio cholerae bacteria, and the enviroment that warrant the interaction. Realities and socioeconomic burden influence spread and control mechanism of the disease. The model investigated some effective ways of hindering cholera outbreak and spread. The existence and uniqueness of solution of the system of equations that the model comprises were ascertained. The basic reproduction number R 0 of the model was obtained using “next-generation matrix” method, and the most sensitive parameters were identified using “normalised forward sensitivity index” method. Three controls, hygiene consciousness denoted by X1, cholera vaccine X2, and cholera awareness programme X3, were chosen. Optimal control theory is applied to ascertain the level of effect of the controls in reducing susceptible, exposed, infected individuals and causative pathogen population. Pontryagin’s maximum principle is used to prove the optimal solution of the model, and the optimal system was derived and numerically solved. Simulations were made with graphs that show the effects of the controls on susceptible, exposed, infected, and Vibrio cholerae population. The findings are that simultaneous application of the three controls can be one of the fast and effective ways of controlling cholera. If two controls are to be selected, hygiene consciousness and vaccine are the best combination.
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来源期刊
Journal of Optimization
Journal of Optimization ENGINEERING, MULTIDISCIPLINARY-
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