{"title":"具有Ornstein-Uhlenbeck过程的随机广义SEI流行病模型的平稳分布和消光","authors":"Tan Su, Xinhong Zhang","doi":"10.1016/j.aml.2023.108690","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we propose a stochastic SEI epidemic model in which the transmission rates are general functions and satisfy the log-normal Ornstein–Uhlenbeck (OU) process. We first theoretically prove that there is a unique positive global solution of this stochastic model. By constructing several suitable Lyapunov functions, the sufficient condition <span><math><mrow><msubsup><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow><mrow><mi>s</mi></mrow></msubsup><mo>></mo><mn>1</mn></mrow></math></span> is established for the existence of stationary distribution. The extinction of disease is also investigated and we find that the disease will die out at an exponential rate when <span><math><mrow><msubsup><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow><mrow><mi>E</mi></mrow></msubsup><mo><</mo><mn>1</mn></mrow></math></span>.</p></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":2.9000,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Stationary distribution and extinction of a stochastic generalized SEI epidemic model with Ornstein–Uhlenbeck process\",\"authors\":\"Tan Su, Xinhong Zhang\",\"doi\":\"10.1016/j.aml.2023.108690\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this paper, we propose a stochastic SEI epidemic model in which the transmission rates are general functions and satisfy the log-normal Ornstein–Uhlenbeck (OU) process. We first theoretically prove that there is a unique positive global solution of this stochastic model. By constructing several suitable Lyapunov functions, the sufficient condition <span><math><mrow><msubsup><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow><mrow><mi>s</mi></mrow></msubsup><mo>></mo><mn>1</mn></mrow></math></span> is established for the existence of stationary distribution. The extinction of disease is also investigated and we find that the disease will die out at an exponential rate when <span><math><mrow><msubsup><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow><mrow><mi>E</mi></mrow></msubsup><mo><</mo><mn>1</mn></mrow></math></span>.</p></div>\",\"PeriodicalId\":55497,\"journal\":{\"name\":\"Applied Mathematics Letters\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.9000,\"publicationDate\":\"2023-09-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Applied Mathematics Letters\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0893965923001222\",\"RegionNum\":2,\"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":"Applied Mathematics Letters","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0893965923001222","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Stationary distribution and extinction of a stochastic generalized SEI epidemic model with Ornstein–Uhlenbeck process
In this paper, we propose a stochastic SEI epidemic model in which the transmission rates are general functions and satisfy the log-normal Ornstein–Uhlenbeck (OU) process. We first theoretically prove that there is a unique positive global solution of this stochastic model. By constructing several suitable Lyapunov functions, the sufficient condition is established for the existence of stationary distribution. The extinction of disease is also investigated and we find that the disease will die out at an exponential rate when .
期刊介绍:
The purpose of Applied Mathematics Letters is to provide a means of rapid publication for important but brief applied mathematical papers. The brief descriptions of any work involving a novel application or utilization of mathematics, or a development in the methodology of applied mathematics is a potential contribution for this journal. This journal''s focus is on applied mathematics topics based on differential equations and linear algebra. Priority will be given to submissions that are likely to appeal to a wide audience.