{"title":"随机易感性-感染易感性模型的截断Wiener过程的分段后退Euler方法的数值分析。","authors":"Xiaochen Yang, Zhanwen Yang, Chiping Zhang","doi":"10.1089/cmb.2022.0462","DOIUrl":null,"url":null,"abstract":"<p><p>This article deals with the numerical positivity, boundedness, convergence, and dynamical behaviors for stochastic susceptible-infected-susceptible (SIS) model. To guarantee the biological significance of the split-step backward Euler method applied to the stochastic SIS model, the numerical positivity and boundedness are investigated by the truncated Wiener process. Motivated by the almost sure boundedness of exact and numerical solutions, the convergence is discussed by the fundamental convergence theorem with a local Lipschitz condition. Moreover, the numerical extinction and persistence are initially obtained by an exponential presentation of the stochastic stability function and strong law of the large number for martingales, which reproduces the existing theoretical results. Finally, numerical examples are given to validate our numerical results for the stochastic SIS model.</p>","PeriodicalId":15526,"journal":{"name":"Journal of Computational Biology","volume":null,"pages":null},"PeriodicalIF":1.4000,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Numerical Analysis of Split-Step Backward Euler Method with Truncated Wiener Process for a Stochastic Susceptible-Infected-Susceptible Model.\",\"authors\":\"Xiaochen Yang, Zhanwen Yang, Chiping Zhang\",\"doi\":\"10.1089/cmb.2022.0462\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p><p>This article deals with the numerical positivity, boundedness, convergence, and dynamical behaviors for stochastic susceptible-infected-susceptible (SIS) model. To guarantee the biological significance of the split-step backward Euler method applied to the stochastic SIS model, the numerical positivity and boundedness are investigated by the truncated Wiener process. Motivated by the almost sure boundedness of exact and numerical solutions, the convergence is discussed by the fundamental convergence theorem with a local Lipschitz condition. Moreover, the numerical extinction and persistence are initially obtained by an exponential presentation of the stochastic stability function and strong law of the large number for martingales, which reproduces the existing theoretical results. Finally, numerical examples are given to validate our numerical results for the stochastic SIS model.</p>\",\"PeriodicalId\":15526,\"journal\":{\"name\":\"Journal of Computational Biology\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.4000,\"publicationDate\":\"2023-10-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Computational Biology\",\"FirstCategoryId\":\"99\",\"ListUrlMain\":\"https://doi.org/10.1089/cmb.2022.0462\",\"RegionNum\":4,\"RegionCategory\":\"生物学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"2023/10/9 0:00:00\",\"PubModel\":\"Epub\",\"JCR\":\"Q4\",\"JCRName\":\"BIOCHEMICAL RESEARCH METHODS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Computational Biology","FirstCategoryId":"99","ListUrlMain":"https://doi.org/10.1089/cmb.2022.0462","RegionNum":4,"RegionCategory":"生物学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2023/10/9 0:00:00","PubModel":"Epub","JCR":"Q4","JCRName":"BIOCHEMICAL RESEARCH METHODS","Score":null,"Total":0}
Numerical Analysis of Split-Step Backward Euler Method with Truncated Wiener Process for a Stochastic Susceptible-Infected-Susceptible Model.
This article deals with the numerical positivity, boundedness, convergence, and dynamical behaviors for stochastic susceptible-infected-susceptible (SIS) model. To guarantee the biological significance of the split-step backward Euler method applied to the stochastic SIS model, the numerical positivity and boundedness are investigated by the truncated Wiener process. Motivated by the almost sure boundedness of exact and numerical solutions, the convergence is discussed by the fundamental convergence theorem with a local Lipschitz condition. Moreover, the numerical extinction and persistence are initially obtained by an exponential presentation of the stochastic stability function and strong law of the large number for martingales, which reproduces the existing theoretical results. Finally, numerical examples are given to validate our numerical results for the stochastic SIS model.
期刊介绍:
Journal of Computational Biology is the leading peer-reviewed journal in computational biology and bioinformatics, publishing in-depth statistical, mathematical, and computational analysis of methods, as well as their practical impact. Available only online, this is an essential journal for scientists and students who want to keep abreast of developments in bioinformatics.
Journal of Computational Biology coverage includes:
-Genomics
-Mathematical modeling and simulation
-Distributed and parallel biological computing
-Designing biological databases
-Pattern matching and pattern detection
-Linking disparate databases and data
-New tools for computational biology
-Relational and object-oriented database technology for bioinformatics
-Biological expert system design and use
-Reasoning by analogy, hypothesis formation, and testing by machine
-Management of biological databases