结核模型的最优控制分析

IF 1.3 4区数学 Q3 BIOLOGY

Journal of Biological Systems Pub Date : 2022-10-21 DOI:10.1142/s0218339022500309

L. L. Obsu

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引用次数: 2

摘要

本文将最优控制理论应用于由非线性常微分方程组控制的结核模型。目的是调查治疗失败对结核病流行的影响。提出了一种最优控制策略，使治疗失败造成的疾病效果和费用最小化。证明了最优控制的存在唯一性。利用庞特里亚金最小值原理解析导出了最优路径的特征。然后使用埃塞俄比亚奥罗米亚州东谢瓦区2010-2019年报告的结核病感染病例拟合控制诱导模型。通过不同的仿真实例与分析结果进行比较。模拟结果表明，通过各种大众媒介的宣传和治疗期间的持续监督的综合作用有助于减少治疗失败，从而减少社区中的结核病流行。

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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OPTIMAL CONTROL ANALYSIS OF A TUBERCULOSIS MODEL

In this paper, an optimal control theory was applied to the tuberculosis (TB) model governed by system of nonlinear ordinary differential equations. The aim is to investigate the impact of treatment failure on the TB epidemic. An optimal control strategy is proposed to minimize the disease effect and cost incurred due to treatment failure. The existence and uniqueness of optimal controls are proved. The characterization of optimal paths is analytically derived using Pontryagin’s Minimum Principle. The control-induced model is then fitted using TB infected cases reported from the year 2010–2019 in East Shewa zone Oromia regional state, Ethiopia. Different simulation cases were performed to compare with analytical results. The simulation results show that the combined effect of awareness via various mass media and continuous supervision during the treatment period helps to reduce treatment failure and hence reduced the TB epidemic in the community.

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来源期刊

Journal of Biological Systems 生物-生物学

CiteScore

2.80

自引率

12.50%

发文量

审稿时长

1 months

期刊介绍： The Journal of Biological Systems is published quarterly. The goal of the Journal is to promote interdisciplinary approaches in Biology and in Medicine, and the study of biological situations with a variety of tools, including mathematical and general systems methods. The Journal solicits original research papers and survey articles in areas that include (but are not limited to): Complex systems studies; isomorphies; nonlinear dynamics; entropy; mathematical tools and systems theories with applications in Biology and Medicine. Interdisciplinary approaches in Biology and Medicine; transfer of methods from one discipline to another; integration of biological levels, from atomic to molecular, macromolecular, cellular, and organic levels; animal biology; plant biology. Environmental studies; relationships between individuals, populations, communities and ecosystems; bioeconomics, management of renewable resources; hierarchy theory; integration of spatial and time scales. Evolutionary biology; co-evolutions; genetics and evolution; branching processes and phyllotaxis. Medical systems; physiology; cardiac modeling; computer models in Medicine; cancer research; epidemiology. Numerical simulations and computations; numerical study and analysis of biological data. Epistemology; history of science. The journal will also publish book reviews.