A Cost-Effective Epidemiological Exposition of Diphtheria Outbreak by the Optimal Control Model: A Case Study of Rohingya Refugee Camp in Bangladesh

IF 1.7 4区 工程技术 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS
Complexity Pub Date : 2024-06-14 DOI:10.1155/2024/6654346
Zahurul Islam, K. M. Ariful Kabir, M. M. Rahman, Md. Atikur Rahman
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Abstract

We consider a deterministic optimal control approach with cost-effectiveness analysis for the diphtheria outbreak in the Rohingya refugee camp in Bangladesh. A deterministic epidemic dynamical model for diphtheria outbreaks has been developed with three optimal controls: vaccination, latent, and infectious treatment. Here, the qualitative study of the model has been interpreted. An objective function has been regarded as a cost function introduced by the optimal controls and the diseases themselves. Then, the existence and uniqueness of the optimal system have also been shown with the help of Pontryagin’s minimum principle. A numerical investigation has been carried out to solve the state and adjoint systems of optimality conditions. Furthermore, it has been investigated using several levels of availability of the optimal controls (vaccination, latent, and infectious treatment) to identify which level gives the best outcomes. Moreover, the cost-effective analysis has been inquired with the numerical value of the cost function and the total cured population in each control strategy to clarify the strategy with the least cost but maximum remediation.

Abstract Image

利用最优控制模型对白喉爆发进行成本效益流行病学阐述:孟加拉国罗辛亚难民营案例研究
我们针对孟加拉国罗辛亚难民营爆发的白喉疫情,考虑了一种具有成本效益分析的确定性最优控制方法。我们建立了一个白喉爆发的确定性流行病动态模型,其中包含三种最优控制方法:疫苗接种、潜伏和传染性治疗。在此,对该模型的定性研究进行了解释。目标函数被视为由最优控制和疾病本身引入的成本函数。然后,借助庞特里亚金最小原理证明了最优系统的存在性和唯一性。为求解最优条件的状态和邻接系统,还进行了数值研究。此外,还使用了几种级别的最优控制(疫苗接种、潜伏和传染性治疗)进行了研究,以确定哪种级别的最优控制效果最好。此外,还利用成本函数的数值和每种控制策略的总治愈人数进行了成本效益分析,以明确成本最低但补救效果最大的策略。
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来源期刊
Complexity
Complexity 综合性期刊-数学跨学科应用
CiteScore
5.80
自引率
4.30%
发文量
595
审稿时长
>12 weeks
期刊介绍: Complexity is a cross-disciplinary journal focusing on the rapidly expanding science of complex adaptive systems. The purpose of the journal is to advance the science of complexity. Articles may deal with such methodological themes as chaos, genetic algorithms, cellular automata, neural networks, and evolutionary game theory. Papers treating applications in any area of natural science or human endeavor are welcome, and especially encouraged are papers integrating conceptual themes and applications that cross traditional disciplinary boundaries. Complexity is not meant to serve as a forum for speculation and vague analogies between words like “chaos,” “self-organization,” and “emergence” that are often used in completely different ways in science and in daily life.
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