{"title":"Persistence and extinction of a stochastic SVI epidemic model with standard incidence and reaction–diffusion","authors":"Tan Su, Yonggui Kao, Daqing Jiang","doi":"10.1016/j.aml.2025.109579","DOIUrl":null,"url":null,"abstract":"<div><div>Considering the important effects of population diffusion and vaccine ineffectiveness on disease transmission, a stochastic SVI (Susceptible–Vaccinated–Infected) epidemic model with reaction–diffusion is mainly investigated in this paper. We prove the existence of the unique global positive strong solution by an innovative variable transformation. The sufficient conditions for disease persistence and exponential extinction are also established by suitable Lyapunov functions.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"168 ","pages":"Article 109579"},"PeriodicalIF":2.8000,"publicationDate":"2025-09-01","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/S0893965925001296","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2025/4/24 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
Considering the important effects of population diffusion and vaccine ineffectiveness on disease transmission, a stochastic SVI (Susceptible–Vaccinated–Infected) epidemic model with reaction–diffusion is mainly investigated in this paper. We prove the existence of the unique global positive strong solution by an innovative variable transformation. The sufficient conditions for disease persistence and exponential extinction are also established by suitable Lyapunov functions.
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.
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