{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,21]],"date-time":"2026-05-21T02:13:44Z","timestamp":1779329624120,"version":"3.51.4"},"reference-count":47,"publisher":"AIP Publishing","issue":"1","funder":[{"DOI":"10.13039\/501100001501","name":"University Grants Commission","doi-asserted-by":"publisher","award":["16-9 (June 2018)\/2019(NET\/CSIR)"],"award-info":[{"award-number":["16-9 (June 2018)\/2019(NET\/CSIR)"]}],"id":[{"id":"10.13039\/501100001501","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001412","name":"Council of Scientific and Industrial Research, India","doi-asserted-by":"publisher","award":["09\/1023(0038)\/2020-EMR-I"],"award-info":[{"award-number":["09\/1023(0038)\/2020-EMR-I"]}],"id":[{"id":"10.13039\/501100001412","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2025,1,1]]},"abstract":"<jats:p>Human immunodeficiency virus (HIV) manifests multiple infections in CD4+ T cells, by binding its envelope proteins to CD4 receptors. Understanding these biological processes is crucial for effective interventions against HIV\/AIDS. Here, we propose a mathematical model that accounts for the multiple infections of CD4+ T cells and an intracellular delay in the dynamics of HIV infection. We study the model system and establish the conditions under which the disease-free equilibrium point and the endemic equilibrium point are locally and globally asymptotically stable. We further provide the conditions under which these equilibrium points undergo forward or backward transcritical bifurcations for the autonomous model and Hopf bifurcation for both the delay model and autonomous models. Our simulation results show that an increase in the rate of multiple infections of CD4+ T cells stabilizes the endemic equilibrium point through Hopf bifurcation. However, in the presence of an intracellular delay, the model system evinces three types of stability scenarios at the endemic equilibrium point\u2014instability switch, stability switch, and stability invariance and is demonstrated using bi-parameter diagrams. One of the novel aspects of this study is exhibiting all these interesting nonlinear dynamical results within a single model incorporating a single time delay.<\/jats:p>","DOI":"10.1063\/5.0232978","type":"journal-article","created":{"date-parts":[[2025,1,10]],"date-time":"2025-01-10T18:11:00Z","timestamp":1736532660000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":3,"title":["Bifurcation and stability analysis of within host HIV dynamics with multiple infections and intracellular delay"],"prefix":"10.1063","volume":"35","author":[{"ORCID":"https:\/\/orcid.org\/0009-0009-2655-649X","authenticated-orcid":false,"given":"Surya","family":"Prakash","sequence":"first","affiliation":[{"name":"Department of Mathematics, Indian Institute of Technology Patna , Patna 801103,","place":["India"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0008-8192-8519","authenticated-orcid":false,"given":"Anuj Kumar","family":"Umrao","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Indian Institute of Technology Patna , Patna 801103,","place":["India"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7651-5639","authenticated-orcid":false,"given":"Prashant K.","family":"Srivastava","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Indian Institute of Technology Patna , Patna 801103,","place":["India"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"317","published-online":{"date-parts":[[2025,1,10]]},"reference":[{"issue":"1","key":"2025011018083783900_c1","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1038\/nrdp.2015.35","article-title":"HIV infection","volume":"1","year":"2015","journal-title":"Nat. Rev. Dis. Primers"},{"issue":"3","key":"2025011018083783900_c2","doi-asserted-by":"publisher","first-page":"245","DOI":"10.1097\/00042560-199803010-00010","article-title":"Direct HIV cytopathicity cannot account for CD4 decline in AIDS in the presence of homeostasis: A worst-case dynamic analysis","volume":"17","year":"1998","journal-title":"J. Acquired Immune Defic. Syndr."},{"key":"2025011018083783900_c3","doi-asserted-by":"publisher","first-page":"430537","DOI":"10.3389\/fgene.2018.00720","article-title":"Interaction of the host and viral genome and their influence on HIV disease","volume":"9","year":"2019","journal-title":"Front. Genet."},{"issue":"13","key":"2025011018083783900_c4","doi-asserted-by":"publisher","first-page":"1881","DOI":"10.1097\/00002030-200309050-00006","article-title":"Persistent immune activation in HIV-1 infection is associated with progression to aids","volume":"17","year":"2003","journal-title":"AIDS"},{"key":"2025011018083783900_c5","doi-asserted-by":"publisher","first-page":"25","DOI":"10.1007\/s11538-008-9351-0","article-title":"A dynamical study of a cellular automata model of the spread of HIV in a lymph node","volume":"71","year":"2009","journal-title":"Bull. Math. Biol."},{"issue":"7","key":"2025011018083783900_c6","doi-asserted-by":"publisher","first-page":"861","DOI":"10.1038\/nm0703-861","article-title":"Immunopathogenesis and immunotherapy in AIDS virus infections","volume":"9","year":"2003","journal-title":"Nat. Med."},{"issue":"7","key":"2025011018083783900_c7","doi-asserted-by":"publisher","first-page":"e1000103","DOI":"10.1371\/journal.pcbi.1000103","article-title":"Dynamics of immune escape during HIV\/SIV infection","volume":"4","year":"2008","journal-title":"PLoS Comput. Biol."},{"issue":"1","key":"2025011018083783900_c8","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.mbs.2005.12.006","article-title":"Estimating kinetic parameters from HIV primary infection data through the eyes of three different mathematical models","volume":"200","year":"2006","journal-title":"Math. Biosci."},{"issue":"1","key":"2025011018083783900_c9","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1137\/S0036144598335107","article-title":"Mathematical analysis of HIV-1 dynamics in vivo","volume":"41","year":"1999","journal-title":"SIAM Rev."},{"key":"2025011018083783900_c10","volume-title":"Virus Dynamics: Mathematical Principles of Immunology and Virology: Mathematical Principles of Immunology and Virology","year":"2000"},{"issue":"5922","key":"2025011018083783900_c11","doi-asserted-by":"publisher","first-page":"1743","DOI":"10.1126\/science.1167525","article-title":"Quantitative 3d video microscopy of HIV transfer across T cell virological synapses","volume":"323","year":"2009","journal-title":"Am. Assoc. Adv. Sci."},{"issue":"12","key":"2025011018083783900_c12","doi-asserted-by":"publisher","first-page":"e1004665","DOI":"10.1371\/journal.pcbi.1004665","article-title":"Modeling the slow CD4+ T cell decline in HIV-infected individuals","volume":"11","year":"2015","journal-title":"PLoS Comput. Biol."},{"key":"2025011018083783900_c13","doi-asserted-by":"publisher","first-page":"516","DOI":"10.1016\/j.amc.2017.08.004","article-title":"Threshold dynamics of an HIV-1 virus model with both virus-to-cell and cell-to-cell transmissions, intracellular delay, and humoral immunity","volume":"315","year":"2017","journal-title":"Appl. Math. Comput."},{"key":"2025011018083783900_c14","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1186\/1471-2148-7-S2-S5","article-title":"Modeling HIV quasispecies evolutionary dynamics","volume":"7","year":"2007","journal-title":"BMC Evol. Biol."},{"issue":"1","key":"2025011018083783900_c15","doi-asserted-by":"publisher","first-page":"281","DOI":"10.1016\/j.jmaa.2006.06.064","article-title":"Global stability and periodic solution of the viral dynamics","volume":"329","year":"2007","journal-title":"J. Math. Anal. Appl."},{"issue":"4","key":"2025011018083783900_c16","first-page":"2257\u20132272","article-title":"Viral dynamics of HIV-1 with CTL immune response","volume":"26","year":"2021","journal-title":"Discrete Contin. Dyn. Syst. Ser. B"},{"issue":"2","key":"2025011018083783900_c17","doi-asserted-by":"publisher","first-page":"1108","DOI":"10.1137\/23M1596004","article-title":"Bistability of an HIV model with immune impairment","volume":"23","year":"2024","journal-title":"SIAM J. Appl. Dyn. Syst."},{"issue":"1","key":"2025011018083783900_c18","doi-asserted-by":"publisher","first-page":"6","DOI":"10.1007\/s00285-024-02104-w","article-title":"A mathematical model for HIV dynamics with multiple infections: Implications for immune escape","volume":"89","year":"2024","journal-title":"J. Math. Biol."},{"key":"2025011018083783900_c19","article-title":"HIV infection dynamics with broadly neutralizing antibodies and CTL immune response","journal-title":"Discrete Contin. Dyn. Syst. S"},{"key":"2025011018083783900_c20","volume-title":"Integrodifferential Equations and Delay Models in Population Dynamics","year":"2013"},{"issue":"1","key":"2025011018083783900_c21","doi-asserted-by":"publisher","first-page":"27","DOI":"10.1016\/S0025-5564(00)00006-7","article-title":"A delay-differential equation model of HIV infection of CD4+ T-cells","volume":"165","year":"2000","journal-title":"Math. Biosci."},{"issue":"1","key":"2025011018083783900_c22","doi-asserted-by":"publisher","first-page":"77","DOI":"10.1097\/00002030-200101050-00012","article-title":"Understanding delay to medical care for HIV infection: The long-term non-presenter","volume":"15","year":"2001","journal-title":"AIDS"},{"issue":"4","key":"2025011018083783900_c23","doi-asserted-by":"publisher","first-page":"779","DOI":"10.4134\/JKMS.2012.49.4.779","article-title":"Global stability of HIV infection models with intracellular delays","volume":"49","year":"2012","journal-title":"J. Korean Math. Soc."},{"issue":"4","key":"2025011018083783900_c24","doi-asserted-by":"publisher","first-page":"3081","DOI":"10.1016\/j.apm.2015.10.003","article-title":"Analysis of an HIV infection model with treatments and delayed immune response","volume":"40","year":"2016","journal-title":"Appl. Math. Modell."},{"issue":"03","key":"2025011018083783900_c25","doi-asserted-by":"publisher","first-page":"421","DOI":"10.1142\/S0218339018500195","article-title":"Effects of eclipse phase and delay on the dynamics of HIV infection","volume":"26","year":"2018","journal-title":"J. Biol. Syst."},{"key":"2025011018083783900_c26","doi-asserted-by":"publisher","first-page":"2450026","DOI":"10.1142\/S1793524524500268","article-title":"Dynamical model of HIV infection with homeostatic growth of CD4+ T cells and immune response","year":"2024","journal-title":"Int. J. Biomath."},{"issue":"14","key":"2025011018083783900_c27","doi-asserted-by":"publisher","first-page":"7247","DOI":"10.1073\/pnas.93.14.7247","article-title":"Viral dynamics in vivo: Limitations on estimates of intracellular delay and virus decay","volume":"93","year":"1996","journal-title":"Proc. Natl. Acad. Sci."},{"issue":"2","key":"2025011018083783900_c28","doi-asserted-by":"publisher","first-page":"143","DOI":"10.1016\/S0025-5564(98)10027-5","article-title":"Influence of delayed viral production on viral dynamics in HIV-1 infected patients","volume":"152","year":"1998","journal-title":"Math. Biosci."},{"issue":"2","key":"2025011018083783900_c29","doi-asserted-by":"publisher","first-page":"99","DOI":"10.1093\/imammb\/dqm010","article-title":"Impact of delays in cell infection and virus production on HIV-1 dynamics","volume":"25","year":"2008","journal-title":"Math. Med. Biol.: J. IMA"},{"issue":"1","key":"2025011018083783900_c30","doi-asserted-by":"publisher","first-page":"57","DOI":"10.3934\/mbe.2021003","article-title":"Global stability of an HIV infection model with saturated CTL immune response and intracellular delay","volume":"18","year":"2021","journal-title":"Math. Biosci. Eng."},{"issue":"1","key":"2025011018083783900_c31","doi-asserted-by":"publisher","first-page":"77","DOI":"10.1007\/s12591-008-0006-2","article-title":"Hopf bifurcation and periodic solutions in a dynamical model for HIV and immune response","volume":"16","year":"2008","journal-title":"Differ. Equ. Dyn. Syst."},{"issue":"2","key":"2025011018083783900_c32","doi-asserted-by":"publisher","first-page":"612","DOI":"10.1016\/j.nonrwa.2008.10.037","article-title":"Modeling the dynamics of HIV and CD4+ T cells during primary infection","volume":"11","year":"2010","journal-title":"Nonlinear Anal.: Real World Appl."},{"key":"2025011018083783900_c33","doi-asserted-by":"publisher","first-page":"385","DOI":"10.1007\/s12591-010-0074-y","article-title":"A primary infection model for HIV and immune response with two discrete time delays","volume":"18","year":"2010","journal-title":"Differ. Equ. Dyn. Syst."},{"issue":"1","key":"2025011018083783900_c34","doi-asserted-by":"publisher","first-page":"146","DOI":"10.1080\/17513758.2017.1408861","article-title":"Stability and Hopf bifurcation for a five-dimensional virus infection model with Beddington\u2013Deangelis incidence and three delays","volume":"12","year":"2018","journal-title":"J. Biol. Dyn."},{"issue":"2","key":"2025011018083783900_c35","doi-asserted-by":"publisher","first-page":"441","DOI":"10.1007\/s10255-022-1088-2","article-title":"A delayed HIV infection model with the homeostatic proliferation of CD4+ T cells","volume":"38","year":"2022","journal-title":"Acta Math. Appl. Sin. Engl. Ser."},{"issue":"5","key":"2025011018083783900_c36","doi-asserted-by":"publisher","first-page":"97","DOI":"10.1007\/s00332-023-09955-5","article-title":"Dynamic behavior of a general stochastic HIV model with virus-to-cell infection, cell-to-cell transmission, immune response and distributed delays","volume":"33","year":"2023","journal-title":"J. Nonlinear Sci."},{"issue":"23","key":"2025011018083783900_c37","doi-asserted-by":"publisher","first-page":"8198","DOI":"10.1073\/pnas.0407498102","article-title":"HIV dynamics with multiple infections of target cells","volume":"102","year":"2005","journal-title":"Proc. Natl. Acad. Sci."},{"issue":"1-2","key":"2025011018083783900_c38","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1016\/S0025-5564(02)00108-6","article-title":"Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission","volume":"180","year":"2002","journal-title":"Math. Biosci."},{"key":"2025011018083783900_c39"},{"key":"2025011018083783900_c40","first-page":"857","article-title":"Compound matrices and ordinary differential equations","volume":"20","year":"1990","journal-title":"Rocky Mt. J. Math."},{"issue":"4","key":"2025011018083783900_c41","doi-asserted-by":"publisher","first-page":"1070","DOI":"10.1137\/S0036141094266449","article-title":"A geometric approach to global-stability problems","volume":"27","year":"1996","journal-title":"SIAM J. Math. Anal."},{"issue":"2","key":"2025011018083783900_c42","doi-asserted-by":"publisher","first-page":"361","DOI":"10.3934\/mbe.2004.1.361","article-title":"Dynamical models of tuberculosis and their applications","volume":"1","year":"2004","journal-title":"Math. Biosci. Eng."},{"issue":"1","key":"2025011018083783900_c43","doi-asserted-by":"publisher","first-page":"250","DOI":"10.1006\/jmaa.1994.1079","article-title":"Criterion of Hopf bifurcations without using eigenvalues","volume":"182","year":"1994","journal-title":"J. Math. Anal. Appl."},{"key":"2025011018083783900_c44"},{"issue":"02","key":"2025011018083783900_c45","doi-asserted-by":"publisher","first-page":"1850027","DOI":"10.1142\/S1793524518500274","article-title":"Modeling the effect of time delay in budget allocation to control an epidemic through awareness","volume":"11","year":"2018","journal-title":"Int. J. Biomath."},{"issue":"2","key":"2025011018083783900_c46","doi-asserted-by":"publisher","first-page":"592","DOI":"10.1016\/0022-247X(82)90243-8","article-title":"Discrete delay, distributed delay and stability switches","volume":"86","year":"1982","journal-title":"J. Math. Anal. Appl."},{"issue":"1","key":"2025011018083783900_c47","doi-asserted-by":"publisher","first-page":"20230111","DOI":"10.1515\/cmb-2023-0111","article-title":"Bifurcation analysis of HIV infection model with cell-to-cell transmission and non-cytolytic cure","volume":"11","year":"2023","journal-title":"Comput. Math. Biophys."}],"container-title":["Chaos: An Interdisciplinary Journal of Nonlinear Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/pubs.aip.org\/aip\/cha\/article-pdf\/doi\/10.1063\/5.0232978\/20342175\/013128_1_5.0232978.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/pubs.aip.org\/aip\/cha\/article-pdf\/doi\/10.1063\/5.0232978\/20342175\/013128_1_5.0232978.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,1,10]],"date-time":"2025-01-10T18:11:04Z","timestamp":1736532664000},"score":1,"resource":{"primary":{"URL":"https:\/\/pubs.aip.org\/cha\/article\/35\/1\/013128\/3330286\/Bifurcation-and-stability-analysis-of-within-host"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,1,1]]},"references-count":47,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2025,1,1]]}},"URL":"https:\/\/doi.org\/10.1063\/5.0232978","relation":{},"ISSN":["1054-1500","1089-7682"],"issn-type":[{"value":"1054-1500","type":"print"},{"value":"1089-7682","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2025,1]]},"published":{"date-parts":[[2025,1,1]]},"article-number":"013128"}}