Amar N. Chatterjee, Teklebirhan Abraha, Fahad Al Basir, Delfim F. M. Torres
{"title":"A model for the dynamics of COVID-19 infection transmission in human with latent delay","authors":"Amar N. Chatterjee, Teklebirhan Abraha, Fahad Al Basir, Delfim F. M. Torres","doi":"10.1007/s13370-024-01226-0","DOIUrl":null,"url":null,"abstract":"<div><p>In this research, we have derived a mathematical model for within human dynamics of COVID-19 infection using delay differential equations. The new model considers a ’latent period’ and ’the time for immune response’ as delay parameters, allowing us to study the effects of time delays in human COVID-19 infection. We have determined the equilibrium points and analyzed their stability. The disease-free equilibrium is stable when the basic reproduction number, <span>\\(R_0\\)</span>, is below unity. Stability switch of the endemic equilibrium occurs through Hopf-bifurcation. This study shows that the effect of latent delay is stabilizing whereas immune response delay has a destabilizing nature.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"36 1","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2025-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Afrika Matematika","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s13370-024-01226-0","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In this research, we have derived a mathematical model for within human dynamics of COVID-19 infection using delay differential equations. The new model considers a ’latent period’ and ’the time for immune response’ as delay parameters, allowing us to study the effects of time delays in human COVID-19 infection. We have determined the equilibrium points and analyzed their stability. The disease-free equilibrium is stable when the basic reproduction number, \(R_0\), is below unity. Stability switch of the endemic equilibrium occurs through Hopf-bifurcation. This study shows that the effect of latent delay is stabilizing whereas immune response delay has a destabilizing nature.