{"title":"Mathematical Analysis of an Industrial HIV/AIDS Model that Incorporates Carefree Attitude Towards Sex","authors":"Baba Seidu, O. D. Makinde, Christopher S. Bornaa","doi":"10.1007/s10441-020-09407-7","DOIUrl":null,"url":null,"abstract":"<div><p>A nonlinear differential equation model is proposed to study the dynamics of HIV/AIDS and its effects on workforce productivity. The disease-free equilibrium point of the model is shown to be locally asymptotically stable when the associated basic reproduction number <span>\\(\\mathcal{{R}}_{0}\\)</span> is less than unity. The model is also shown to exhibit multiple endemic states for some parameter values when <span>\\(\\mathcal{{R}}_{0}<1\\)</span> and <span>\\(\\mathcal{{R}}_{0}>1\\)</span>. Global asymptotic stability of the disease-free equilibrium is guaranteed only when the fractions of the Susceptible subclass populations are within some bounds. Optimal control analysis of the model revealed that the most cost effective strategy that should be adopted in the fight against HIV/AIDS spread within the workforce is one that seeks to prevent infections and the treatment of infected individuals.</p></div>","PeriodicalId":7057,"journal":{"name":"Acta Biotheoretica","volume":null,"pages":null},"PeriodicalIF":1.4000,"publicationDate":"2021-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s10441-020-09407-7","citationCount":"7","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Biotheoretica","FirstCategoryId":"99","ListUrlMain":"https://link.springer.com/article/10.1007/s10441-020-09407-7","RegionNum":4,"RegionCategory":"生物学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICAL & COMPUTATIONAL BIOLOGY","Score":null,"Total":0}
引用次数: 7
Abstract
A nonlinear differential equation model is proposed to study the dynamics of HIV/AIDS and its effects on workforce productivity. The disease-free equilibrium point of the model is shown to be locally asymptotically stable when the associated basic reproduction number \(\mathcal{{R}}_{0}\) is less than unity. The model is also shown to exhibit multiple endemic states for some parameter values when \(\mathcal{{R}}_{0}<1\) and \(\mathcal{{R}}_{0}>1\). Global asymptotic stability of the disease-free equilibrium is guaranteed only when the fractions of the Susceptible subclass populations are within some bounds. Optimal control analysis of the model revealed that the most cost effective strategy that should be adopted in the fight against HIV/AIDS spread within the workforce is one that seeks to prevent infections and the treatment of infected individuals.
期刊介绍：
Acta Biotheoretica is devoted to the promotion of theoretical biology, encompassing mathematical biology and the philosophy of biology, paying special attention to the methodology of formation of biological theory.
Papers on all kind of biological theories are welcome. Interesting subjects include philosophy of biology, biomathematics, computational biology, genetics, ecology and morphology. The process of theory formation can be presented in verbal or mathematical form. Moreover, purely methodological papers can be devoted to the historical origins of the philosophy underlying biological theories and concepts.
Papers should contain clear statements of biological assumptions, and where applicable, a justification of their translation into mathematical form and a detailed discussion of the mathematical treatment. The connection to empirical data should be clarified.
Acta Biotheoretica also welcomes critical book reviews, short comments on previous papers and short notes directing attention to interesting new theoretical ideas.
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