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Optimal Control Strategies and Sensitivity Analysis of an HIV/AIDS-Resistant Model with Behavior Change
Acta Biotheoretica ( IF 1.3 ) Pub Date : 2021-07-30 , DOI: 10.1007/s10441-021-09421-3
Musa Rabiu 1 , Robert Willie 1 , Nabendra Parumasur 1
Affiliation  

Despite several research on HIV/AIDS, it is still incumbent to investigate more effective control measures to mitigate its infection level. Therefore, we introduce an HIV/AIDS-resistant model with behavior change and study its basic properties. In order to determine the most sensitive parameters that are responsible for disease transmission with respect to the basic reproduction number and those responsible for disease prevalence with respect to the endemic equilibrium, the sensitivity analysis was established and it was confirmed that the influx rate of people into the infected population and total abstinence from all risk practices and endemic areas are some of the most sensitive parameters for disease spread and disease eradication, respectively. Furthermore, by considering controls \(u_1\) denoting the government’s intervention in promoting and encouraging behavior change, \(u_2\) representing intake of balanced nutritional supplementation, and \(u_3\) connoting antiretroviral therapy (ART), an optimal control problem was developed and analyzed. Before the establishment of the necessary conditions of the optimal control using Pontryagin’s Maximum Principle, we proved the existence of the optimal control triplet \((u_1(t),u_2(t),u_3(t)\in \Phi ,\) where \(\Phi\) is the control set at time t,) which has been neglected by many researchers in recent years. Using the Runge–Kutta scheme, the optimal control problem was solved to understand the best combination of control strategies. Using the demographic and epidemiological data for South Africa on HIV/AIDS, a numerical simulation was carried out and results are presented on 3D surface plots. The obtained results suggested that the combination of all the considered control measures is the best method to ensure disease eradication.



中文翻译:

具有行为改变的抗 HIV/AIDS 模型的最优控制策略和敏感性分析

尽管对 HIV/AIDS 进行了多项研究,但仍有责任研究更有效的控制措施以降低其感染水平。因此,我们引入了一个具有行为改变的抗 HIV/AIDS 模型并研究其基本特性。为了确定与基本繁殖数相关的疾病传播的最敏感参数和与地方病平衡相关的疾病流行的最敏感参数,建立了敏感性分析,并证实了人们进入感染人群和完全戒除所有风险做法和流行地区分别是疾病传播和根除疾病的一些最敏感的参数。此外,通过考虑控制\(u_1\)表示政府干预促进和鼓励行为改变,\(u_2\)表示摄入均衡的营养补充剂,\(u_3\) 表示抗逆转录病毒疗法 (ART),开发和分析了一个最优控制问题。在利用庞特里亚金最大原理建立最优控制的必要条件之前,我们证明了最优控制三元组\((u_1(t),u_2(t),u_3(t)\in\Phi,\)的存在性\(\Phi\)t时刻的控制集,) 近年来被许多研究人员所忽视。使用 Runge-Kutta 方案,解决了最优控制问题以了解控制策略的最佳组合。使用南非艾滋病毒/艾滋病的人口统计和流行病学数据,进行了数值模拟,结果显示在 3D 表面图上。获得的结果表明,所有考虑的控制措施的结合是确保疾病根除的最佳方法。

更新日期:2021-08-01
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