二次感染 SIRS 模型的几何分析

IF 1.9 4区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Applied Mathematics Pub Date : 2024-04-09 DOI:10.1137/23m1565632

Panagiotis Kaklamanos, Andrea Pugliese, Mattia Sensi, Sara Sottile

{"title":"二次感染 SIRS 模型的几何分析","authors":"Panagiotis Kaklamanos, Andrea Pugliese, Mattia Sensi, Sara Sottile","doi":"10.1137/23m1565632","DOIUrl":null,"url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 2, Page 661-686, April 2024. <br/> Abstract. We propose a compartmental model for a disease with temporary immunity and secondary infections. From our assumptions on the parameters involved in the model, the system naturally evolves in three time scales. We characterize the equilibria of the system and analyze their stability. We find conditions for the existence of two endemic equilibria for some cases in which [math]. Then, we unravel the interplay of the three time scales, providing conditions to foresee whether the system evolves in all three scales, or only in the fast and the intermediate ones. We conclude with numerical simulations and bifurcation analysis to complement our analytical results.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.9000,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A Geometric Analysis of the SIRS Model with Secondary Infections\",\"authors\":\"Panagiotis Kaklamanos, Andrea Pugliese, Mattia Sensi, Sara Sottile\",\"doi\":\"10.1137/23m1565632\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"SIAM Journal on Applied Mathematics, Volume 84, Issue 2, Page 661-686, April 2024. <br/> Abstract. We propose a compartmental model for a disease with temporary immunity and secondary infections. From our assumptions on the parameters involved in the model, the system naturally evolves in three time scales. We characterize the equilibria of the system and analyze their stability. We find conditions for the existence of two endemic equilibria for some cases in which [math]. Then, we unravel the interplay of the three time scales, providing conditions to foresee whether the system evolves in all three scales, or only in the fast and the intermediate ones. We conclude with numerical simulations and bifurcation analysis to complement our analytical results.\",\"PeriodicalId\":51149,\"journal\":{\"name\":\"SIAM Journal on Applied Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.9000,\"publicationDate\":\"2024-04-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"SIAM Journal on Applied Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1137/23m1565632\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIAM Journal on Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1137/23m1565632","RegionNum":4,"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

摘要

SIAM 应用数学杂志》第 84 卷第 2 期第 661-686 页，2024 年 4 月。摘要。我们提出了一种具有暂时免疫和二次感染的疾病分区模型。根据我们对模型相关参数的假设，该系统在三个时间尺度上自然演化。我们描述了该系统的均衡状态并分析了其稳定性。我们找到了在某些情况下存在两个地方性均衡的条件[math]。然后，我们揭示了三个时间尺度的相互作用，为预测系统是在所有三个尺度上演化，还是只在快速和中间尺度上演化提供了条件。最后，我们通过数值模拟和分岔分析来补充我们的分析结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

A Geometric Analysis of the SIRS Model with Secondary Infections

SIAM Journal on Applied Mathematics, Volume 84, Issue 2, Page 661-686, April 2024.
Abstract. We propose a compartmental model for a disease with temporary immunity and secondary infections. From our assumptions on the parameters involved in the model, the system naturally evolves in three time scales. We characterize the equilibria of the system and analyze their stability. We find conditions for the existence of two endemic equilibria for some cases in which [math]. Then, we unravel the interplay of the three time scales, providing conditions to foresee whether the system evolves in all three scales, or only in the fast and the intermediate ones. We conclude with numerical simulations and bifurcation analysis to complement our analytical results.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

SIAM Journal on Applied Mathematics 数学-应用数学

CiteScore

3.60

自引率

0.00%

发文量

审稿时长

12 months

期刊介绍： SIAM Journal on Applied Mathematics (SIAP) is an interdisciplinary journal containing research articles that treat scientific problems using methods that are of mathematical interest. Appropriate subject areas include the physical, engineering, financial, and life sciences. Examples are problems in fluid mechanics, including reaction-diffusion problems, sedimentation, combustion, and transport theory; solid mechanics; elasticity; electromagnetic theory and optics; materials science; mathematical biology, including population dynamics, biomechanics, and physiology; linear and nonlinear wave propagation, including scattering theory and wave propagation in random media; inverse problems; nonlinear dynamics; and stochastic processes, including queueing theory. Mathematical techniques of interest include asymptotic methods, bifurcation theory, dynamical systems theory, complex network theory, computational methods, and probabilistic and statistical methods.