{"title":"A novel stochastic Hepatitis B virus epidemic model with second-order multiplicative α-stable noise and real data","authors":"","doi":"10.1007/s10473-024-0220-1","DOIUrl":null,"url":null,"abstract":"<h3>Abstract</h3> <p>This work presents an advanced and detailed analysis of the mechanisms of hepatitis B virus (HBV) propagation in an environment characterized by variability and stochas-ticity. Based on some biological features of the virus and the assumptions, the corresponding deterministic model is formulated, which takes into consideration the effect of vaccination. This deterministic model is extended to a stochastic framework by considering a new form of disturbance which makes it possible to simulate strong and significant fluctuations. The long-term behaviors of the virus are predicted by using stochastic differential equations with second-order multiplicative <em>α</em>-stable jumps. By developing the assumptions and employing the novel theoretical tools, the threshold parameter responsible for ergodicity (persistence) and extinction is provided. The theoretical results of the current study are validated by numerical simulations and parameters estimation is also performed. Moreover, we obtain the following new interesting findings: (a) in each class, the average time depends on the value of <em>α</em>; (b) the second-order noise has an inverse effect on the spread of the virus; (c) the shapes of population densities at stationary level quickly changes at certain values of <em>α</em>. The last three conclusions can provide a solid research base for further investigation in the field of biological and ecological modeling.</p>","PeriodicalId":50998,"journal":{"name":"Acta Mathematica Scientia","volume":null,"pages":null},"PeriodicalIF":1.2000,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mathematica Scientia","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10473-024-0220-1","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
This work presents an advanced and detailed analysis of the mechanisms of hepatitis B virus (HBV) propagation in an environment characterized by variability and stochas-ticity. Based on some biological features of the virus and the assumptions, the corresponding deterministic model is formulated, which takes into consideration the effect of vaccination. This deterministic model is extended to a stochastic framework by considering a new form of disturbance which makes it possible to simulate strong and significant fluctuations. The long-term behaviors of the virus are predicted by using stochastic differential equations with second-order multiplicative α-stable jumps. By developing the assumptions and employing the novel theoretical tools, the threshold parameter responsible for ergodicity (persistence) and extinction is provided. The theoretical results of the current study are validated by numerical simulations and parameters estimation is also performed. Moreover, we obtain the following new interesting findings: (a) in each class, the average time depends on the value of α; (b) the second-order noise has an inverse effect on the spread of the virus; (c) the shapes of population densities at stationary level quickly changes at certain values of α. The last three conclusions can provide a solid research base for further investigation in the field of biological and ecological modeling.
期刊介绍：
Acta Mathematica Scientia was founded by Prof. Li Guoping (Lee Kwok Ping) in April 1981.
The aim of Acta Mathematica Scientia is to present to the specialized readers important new achievements in the areas of mathematical sciences. The journal considers for publication of original research papers in all areas related to the frontier branches of mathematics with other science and technology.
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