{"title":"Asymptotic comportment of a stochastic SIQR model with mean-reverting inhomogeneous geometric Brownian motion","authors":"","doi":"10.28919/cmbn/8195","DOIUrl":null,"url":null,"abstract":"The object of this work is to analyze the dynamical behavior of an SIQR epidemic model incorporating the mean-reverting inhomogeneous geometric Brownian motion process (IGBM for short). As a first step, we prove that a global-in-time solution exists, and we show equally that it is unique and positive. Then, we find out an appropriate hypothetical framework leading to the existence of an ergodic stationary distribution. After that, we provide certain sufficient conditions for the disease’s exponential extinction, and we show that they match those of the deterministic version in this case. Finally, we outline some numerical simulation examples to back up our theoretical outcomes.","PeriodicalId":44079,"journal":{"name":"Communications in Mathematical Biology and Neuroscience","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Mathematical Biology and Neuroscience","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.28919/cmbn/8195","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, INFORMATION SYSTEMS","Score":null,"Total":0}
引用次数: 0
Abstract
The object of this work is to analyze the dynamical behavior of an SIQR epidemic model incorporating the mean-reverting inhomogeneous geometric Brownian motion process (IGBM for short). As a first step, we prove that a global-in-time solution exists, and we show equally that it is unique and positive. Then, we find out an appropriate hypothetical framework leading to the existence of an ergodic stationary distribution. After that, we provide certain sufficient conditions for the disease’s exponential extinction, and we show that they match those of the deterministic version in this case. Finally, we outline some numerical simulation examples to back up our theoretical outcomes.
期刊介绍:
Communications in Mathematical Biology and Neuroscience (CMBN) is a peer-reviewed open access international journal, which is aimed to provide a publication forum for important research in all aspects of mathematical biology and neuroscience. This journal will accept high quality articles containing original research results and survey articles of exceptional merit.