Regional optimization problem for a general reaction–diffusion malaria model with temperature and rainfall

IF 2.5 3区 计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS
Jing Wang, Hongyong Zhao
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引用次数: 0

Abstract

This work primarily addresses the regional optimization problem of a malaria model in heterogeneous environments, which incorporates general incidence rate, vaccination, temperature and rainfall. To reflect the differences in resource allocation across different regions and times, the upper bound of control is extended to a bounded function related to spatial location and time. On this basis, a control problem is investigated, with the goal of minimizing the discrepancy between the actual and desired control outcomes for mosquitoes and infectious humans, and the associated costs. Firstly, the application of truncation technique and semigroup theory enables us to obtain the existence, uniqueness and some estimates of the positive strong solution for the controlled system. Despite the intricate nature of the controlled system, which makes proving global solvability challenging, this hurdle is successfully overcome. Subsequently, applying the technique of minimizing sequence, the existence of optimal pair is demonstrated. By utilizing the differentiability of control-to-state mapping, we establish the first-order necessary optimality condition. Specifically, deeper insights are offered in the left neighborhood of the terminal moment. Furthermore, provide the second-order necessary and sufficient optimality conditions. Finally, explore the spread and control of malaria in The Gambia. The analysis shows that the upper bound of control possesses a remarkable influence on its optimal form. Moreover, temperature and rainfall can significantly affect costs and benefits of control measures, thereby affecting the evaluation process. These outcomes enrich and generalize the study on regional optimal control problems of disease models, and provide new perspectives for related research.
这项工作主要解决了异质性环境下疟疾模型的区域优化问题,其中包括一般发病率,疫苗接种,温度和降雨量。为了反映不同地区和时间资源配置的差异,将控制上界扩展为与空间位置和时间相关的有界函数。在此基础上,研究了一个控制问题,目标是尽量减少蚊子和感染人类的实际控制结果与期望控制结果之间的差异,并减少相关成本。首先,利用截断技术和半群理论,得到了被控系统正强解的存在唯一性和一些估计;尽管受控系统的复杂性使得证明全局可解性具有挑战性,但这一障碍已被成功克服。然后,利用最小序列技术,证明了最优对的存在性。利用控制-状态映射的可微性,建立了一阶必要最优性条件。具体来说,在终端时刻的左侧邻域提供了更深入的见解。进一步给出了二阶充分必要最优性条件。最后,探索疟疾在冈比亚的传播和控制。分析表明,控制上界对其最优形式有显著影响。此外,温度和降雨量会显著影响控制措施的成本和效益,从而影响评价过程。这些成果丰富和推广了疾病模型区域最优控制问题的研究,为相关研究提供了新的视角。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
European Journal of Control
European Journal of Control 工程技术-自动化与控制系统
CiteScore
5.80
自引率
5.90%
发文量
131
审稿时长
1 months
期刊介绍: The European Control Association (EUCA) has among its objectives to promote the development of the discipline. Apart from the European Control Conferences, the European Journal of Control is the Association''s main channel for the dissemination of important contributions in the field. The aim of the Journal is to publish high quality papers on the theory and practice of control and systems engineering. The scope of the Journal will be wide and cover all aspects of the discipline including methodologies, techniques and applications. Research in control and systems engineering is necessary to develop new concepts and tools which enhance our understanding and improve our ability to design and implement high performance control systems. Submitted papers should stress the practical motivations and relevance of their results. The design and implementation of a successful control system requires the use of a range of techniques: Modelling Robustness Analysis Identification Optimization Control Law Design Numerical analysis Fault Detection, and so on.
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