{"title":"Modeling the effects of contact tracing on COVID-19 transmission.","authors":"Ali Traoré, Fourtoua Victorien Konané","doi":"10.1186/s13662-020-02972-8","DOIUrl":null,"url":null,"abstract":"<p><p>In this paper, a mathematical model for COVID-19 that involves contact tracing is studied. The <i>contact tracing-induced</i> reproduction number <math><msub><mi>R</mi> <mi>q</mi></msub> </math> and equilibrium for the model are determined and stabilities are examined. The global stabilities results are achieved by constructing Lyapunov functions. The <i>contact tracing-induced</i> reproduction number <math><msub><mi>R</mi> <mi>q</mi></msub> </math> is compared with the basic reproduction number <math><msub><mi>R</mi> <mn>0</mn></msub> </math> for the model in the absence of any intervention to assess the possible benefits of the contact tracing strategy.</p>","PeriodicalId":53311,"journal":{"name":"Advances in Difference Equations","volume":null,"pages":null},"PeriodicalIF":4.1000,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s13662-020-02972-8","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Difference Equations","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1186/s13662-020-02972-8","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2020/9/21 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 1
Abstract
In this paper, a mathematical model for COVID-19 that involves contact tracing is studied. The contact tracing-induced reproduction number and equilibrium for the model are determined and stabilities are examined. The global stabilities results are achieved by constructing Lyapunov functions. The contact tracing-induced reproduction number is compared with the basic reproduction number for the model in the absence of any intervention to assess the possible benefits of the contact tracing strategy.
期刊介绍：
The theory of difference equations, the methods used, and their wide applications have advanced beyond their adolescent stage to occupy a central position in applicable analysis. In fact, in the last 15 years, the proliferation of the subject has been witnessed by hundreds of research articles, several monographs, many international conferences, and numerous special sessions.
The theory of differential and difference equations forms two extreme representations of real world problems. For example, a simple population model when represented as a differential equation shows the good behavior of solutions whereas the corresponding discrete analogue shows the chaotic behavior. The actual behavior of the population is somewhere in between.
The aim of Advances in Difference Equations is to report mainly the new developments in the field of difference equations, and their applications in all fields. We will also consider research articles emphasizing the qualitative behavior of solutions of ordinary, partial, delay, fractional, abstract, stochastic, fuzzy, and set-valued differential equations.
Advances in Difference Equations will accept high-quality articles containing original research results and survey articles of exceptional merit.
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