{"title":"具有内在增长率的 SEIR 流行病模型中的松弛震荡","authors":"Yingying Zhang, Ruohan Wang, Yanan Cai","doi":"10.1155/2024/5373794","DOIUrl":null,"url":null,"abstract":"<div>\n <p>The periodic oscillation transmission of infectious diseases is widespread, deep understanding of this periodic pattern and exploring the generation mechanism, and identifying the specific factors that lead to such periodic outbreaks, which are of very importanceto predict and control the spread of infectious diseases. In this study, to further reveal the mathematical mechanism of spontaneous generation of periodic oscillation solution, we investigate a type of SEIR epidemic model with a small intrinsic growth rate. By utilizing the singular perturbation theory and center manifold theorem, we extend the relaxation oscillation of three-dimensional SIR models to the four-dimensional SEIR models and prove the existence of stable relaxation oscillation with a large amplitude in the model. Numerical simulations are performed to verify our theoretical results. The results presented in this study provide a new idea for the study of the intrinsic mechanism of periodic oscillation in epidemiology, enrich the dynamics of epidemic models, and deepen the understanding of the global dynamics of these models.</p>\n </div>","PeriodicalId":50653,"journal":{"name":"Complexity","volume":"2024 1","pages":""},"PeriodicalIF":1.7000,"publicationDate":"2024-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1155/2024/5373794","citationCount":"0","resultStr":"{\"title\":\"Relaxation Oscillation in SEIR Epidemic Models with the Intrinsic Growth Rate\",\"authors\":\"Yingying Zhang, Ruohan Wang, Yanan Cai\",\"doi\":\"10.1155/2024/5373794\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div>\\n <p>The periodic oscillation transmission of infectious diseases is widespread, deep understanding of this periodic pattern and exploring the generation mechanism, and identifying the specific factors that lead to such periodic outbreaks, which are of very importanceto predict and control the spread of infectious diseases. In this study, to further reveal the mathematical mechanism of spontaneous generation of periodic oscillation solution, we investigate a type of SEIR epidemic model with a small intrinsic growth rate. By utilizing the singular perturbation theory and center manifold theorem, we extend the relaxation oscillation of three-dimensional SIR models to the four-dimensional SEIR models and prove the existence of stable relaxation oscillation with a large amplitude in the model. Numerical simulations are performed to verify our theoretical results. The results presented in this study provide a new idea for the study of the intrinsic mechanism of periodic oscillation in epidemiology, enrich the dynamics of epidemic models, and deepen the understanding of the global dynamics of these models.</p>\\n </div>\",\"PeriodicalId\":50653,\"journal\":{\"name\":\"Complexity\",\"volume\":\"2024 1\",\"pages\":\"\"},\"PeriodicalIF\":1.7000,\"publicationDate\":\"2024-06-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://onlinelibrary.wiley.com/doi/epdf/10.1155/2024/5373794\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Complexity\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1155/2024/5373794\",\"RegionNum\":4,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Complexity","FirstCategoryId":"5","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1155/2024/5373794","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 0
摘要
传染病的周期性振荡传播十分普遍,深入理解这种周期性模式并探索其产生机制,找出导致这种周期性爆发的特定因素,对于预测和控制传染病的传播具有十分重要的意义。在本研究中,为了进一步揭示周期振荡解自发产生的数学机制,我们研究了一种具有较小固有增长率的 SEIR 流行病模型。利用奇异扰动理论和中心流形定理,我们将三维 SIR 模型的弛豫振荡扩展到四维 SEIR 模型,并证明了模型中存在振幅较大的稳定弛豫振荡。我们还进行了数值模拟来验证我们的理论结果。本研究的结果为研究流行病学中周期振荡的内在机理提供了新思路,丰富了流行病模型的动力学内容,加深了对这些模型全局动力学的理解。
Relaxation Oscillation in SEIR Epidemic Models with the Intrinsic Growth Rate
The periodic oscillation transmission of infectious diseases is widespread, deep understanding of this periodic pattern and exploring the generation mechanism, and identifying the specific factors that lead to such periodic outbreaks, which are of very importanceto predict and control the spread of infectious diseases. In this study, to further reveal the mathematical mechanism of spontaneous generation of periodic oscillation solution, we investigate a type of SEIR epidemic model with a small intrinsic growth rate. By utilizing the singular perturbation theory and center manifold theorem, we extend the relaxation oscillation of three-dimensional SIR models to the four-dimensional SEIR models and prove the existence of stable relaxation oscillation with a large amplitude in the model. Numerical simulations are performed to verify our theoretical results. The results presented in this study provide a new idea for the study of the intrinsic mechanism of periodic oscillation in epidemiology, enrich the dynamics of epidemic models, and deepen the understanding of the global dynamics of these models.
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.