DYNAMICAL ANALYSIS OF TB MODEL WITH NONLINEAR INCIDENCE RATE AND OPTIMAL CONTROL

IF 1.3 4区数学 Q3 BIOLOGY

Journal of Biological Systems Pub Date : 2023-04-25 DOI:10.1142/s0218339023500250

Shuping Li, Huafang Liu

引用次数: 0

Abstract

We propose and analyze a TB transmission model with nonlinear incidence rate, immunization and medical treatment. First, the existences and stabilities of the equilibrium are studied. The results indicate the basic reproduction number [Formula: see text] is the threshold of disease extinction and persistence. The disease-free equilibrium is globally asymptotically stable when [Formula: see text], and the disease will gradually disappear. The unique positive equilibrium is local stability and the disease is uniformly persistent when [Formula: see text]. Second, optimal control is added to the original model because of limited resources. Finally, the stability of the equilibrium and the theoretical results of optimal control are verified by numerical simulations, and the sensitivity of the parameters is analyzed by the PRCC method.

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具有非线性发病率的TB模型动力学分析及最优控制

我们提出并分析了一个具有非线性发病率、免疫和医疗的结核病传播模型。首先，研究了平衡的存在性和稳定性。结果表明，基本繁殖数[公式：见正文]是疾病灭绝和持续的阈值。当[公式：见正文]时，无病平衡是全局渐近稳定的，疾病将逐渐消失。唯一的正平衡是局部稳定性，当[公式：见正文]时，疾病是一致持久的。其次，由于资源有限，最优控制被添加到原始模型中。最后，通过数值模拟验证了平衡的稳定性和最优控制的理论结果，并用PRCC方法分析了参数的敏感性。

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

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.