{"title":"Behavior of Trajectories of a Four-Dimensional Model of HIV Infection","authors":"A. N. Kanatnikov, O. S. Tkacheva","doi":"10.1134/s00122661230110022","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> A model of interaction between the human immunodeficiency virus and the human\nimmune system is considered. Equilibria in the state space of the system and their stability are\nanalyzed, and the ultimate bounds of the trajectories are constructed. It has been proved that the\nlocal asymptotic stability of the equilibrium corresponding to the absence of disease is equivalent\nto its global asymptotic stability. The loss of stability is shown to be caused by a transcritical\nbifurcation.\n</p>","PeriodicalId":50580,"journal":{"name":"Differential Equations","volume":"4 1","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2023-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Differential Equations","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s00122661230110022","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
A model of interaction between the human immunodeficiency virus and the human
immune system is considered. Equilibria in the state space of the system and their stability are
analyzed, and the ultimate bounds of the trajectories are constructed. It has been proved that the
local asymptotic stability of the equilibrium corresponding to the absence of disease is equivalent
to its global asymptotic stability. The loss of stability is shown to be caused by a transcritical
bifurcation.
期刊介绍：
Differential Equations is a journal devoted to differential equations and the associated integral equations. The journal publishes original articles by authors from all countries and accepts manuscripts in English and Russian. The topics of the journal cover ordinary differential equations, partial differential equations, spectral theory of differential operators, integral and integral–differential equations, difference equations and their applications in control theory, mathematical modeling, shell theory, informatics, and oscillation theory. The journal is published in collaboration with the Department of Mathematics and the Division of Nanotechnologies and Information Technologies of the Russian Academy of Sciences and the Institute of Mathematics of the National Academy of Sciences of Belarus.
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