Global analyses of a ratio-dependent state feedback control system for infectious disease

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-07-09 DOI:10.1016/j.cnsns.2025.109068

Chenxi Huang, Qianqian Zhang, Sanyi Tang

{"title":"Global analyses of a ratio-dependent state feedback control system for infectious disease","authors":"Chenxi Huang, Qianqian Zhang, Sanyi Tang","doi":"10.1016/j.cnsns.2025.109068","DOIUrl":null,"url":null,"abstract":"<div><div>This paper constructs a state feedback control system grounded in the SIS model to study infectious disease prevention and control measures. A proportional threshold is defined: when the proportion of infected individuals is below the threshold, no interventions will be carried out. However, once the proportion exceeds the predefined threshold, measures like vaccination and isolation will be initiated. After clarifying the ODE system properties, the Poincaré map is defined and classified. Its properties like domain, range, and monotonicity are studied to analyze positive periodic solutions (PSs). We find that if the boundary equilibrium is globally stable and there exists no endemic equilibrium, the state feedback control SIS system, i.e., IDE system, does not possess PSs. When the endemic equilibrium is unique and stable, conditions for the existence and stability of the order-1 positive PS are presented, and the higher-order solutions may exist. What is more, if the endemic equilibrium is unique and unstable, and the ODE system generates a stable limit cycle, the conditions for the existence of order-<span><math><mi>k</mi></math></span> PSs for the IDE system are similarly derived. Finally, through numerical simulations, this study demonstrates that when the endemic equilibrium is unique and unstable, the IDE system exhibits complex bifurcation behavior in response to key control parameters, including period-doubling bifurcations, period-halving bifurcations, and chaos.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"151 ","pages":"Article 109068"},"PeriodicalIF":3.4000,"publicationDate":"2025-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Nonlinear Science and Numerical Simulation","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1007570425004794","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

Abstract

This paper constructs a state feedback control system grounded in the SIS model to study infectious disease prevention and control measures. A proportional threshold is defined: when the proportion of infected individuals is below the threshold, no interventions will be carried out. However, once the proportion exceeds the predefined threshold, measures like vaccination and isolation will be initiated. After clarifying the ODE system properties, the Poincaré map is defined and classified. Its properties like domain, range, and monotonicity are studied to analyze positive periodic solutions (PSs). We find that if the boundary equilibrium is globally stable and there exists no endemic equilibrium, the state feedback control SIS system, i.e., IDE system, does not possess PSs. When the endemic equilibrium is unique and stable, conditions for the existence and stability of the order-1 positive PS are presented, and the higher-order solutions may exist. What is more, if the endemic equilibrium is unique and unstable, and the ODE system generates a stable limit cycle, the conditions for the existence of order-

k

PSs for the IDE system are similarly derived. Finally, through numerical simulations, this study demonstrates that when the endemic equilibrium is unique and unstable, the IDE system exhibits complex bifurcation behavior in response to key control parameters, including period-doubling bifurcations, period-halving bifurcations, and chaos.

查看原文本刊更多论文

传染病比率依赖状态反馈控制系统的全局分析

本文构建了一个基于SIS模型的状态反馈控制系统来研究传染病的防控措施。定义了一个比例阈值：当受感染个体的比例低于该阈值时，将不进行干预。但是，一旦比例超过预定的阈值，将启动疫苗接种和隔离等措施。在澄清了ODE系统属性之后，定义并分类了poincar映射。研究了正周期解的定义域、值域和单调性等性质。我们发现，如果边界平衡是全局稳定的，并且不存在地方性平衡，则状态反馈控制SIS系统即IDE系统不具有PSs。当地方性平衡是唯一且稳定时，给出了1阶正PS存在和稳定的条件，并且可能存在高阶解。此外，如果局部平衡点是唯一且不稳定的，并且ODE系统产生一个稳定的极限环，则同样导出了IDE系统存在k阶ps的条件。最后，通过数值模拟，研究表明，当地方性平衡是唯一且不稳定时，IDE系统对关键控制参数的响应表现出复杂的分岔行为，包括倍周期分岔、减半周期分岔和混沌。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Communications in Nonlinear Science and Numerical Simulation MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

6.80

自引率

7.70%

发文量

378

审稿时长

78 days

期刊介绍： The journal publishes original research findings on experimental observation, mathematical modeling, theoretical analysis and numerical simulation, for more accurate description, better prediction or novel application, of nonlinear phenomena in science and engineering. It offers a venue for researchers to make rapid exchange of ideas and techniques in nonlinear science and complexity. The submission of manuscripts with cross-disciplinary approaches in nonlinear science and complexity is particularly encouraged. Topics of interest: Nonlinear differential or delay equations, Lie group analysis and asymptotic methods, Discontinuous systems, Fractals, Fractional calculus and dynamics, Nonlinear effects in quantum mechanics, Nonlinear stochastic processes, Experimental nonlinear science, Time-series and signal analysis, Computational methods and simulations in nonlinear science and engineering, Control of dynamical systems, Synchronization, Lyapunov analysis, High-dimensional chaos and turbulence, Chaos in Hamiltonian systems, Integrable systems and solitons, Collective behavior in many-body systems, Biological physics and networks, Nonlinear mechanical systems, Complex systems and complexity. No length limitation for contributions is set, but only concisely written manuscripts are published. Brief papers are published on the basis of Rapid Communications. Discussions of previously published papers are welcome.