Stability and bifurcation analysis of an HIV-1 infection model with a general incidence and CTL immune response
In this paper, with eclipse stage in consideration, we propose an HIV-1 infection model with a general incidence rate and CTL immune response. We first study the existence and local stability of equilibria, which is characterized by the basic infection reproduction number and the basic immunity repr...
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| Veröffentlicht in: | Journal of biological dynamics 2021-01, Vol.15 (1), p.367-394 |
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| creator | Ma, Xinsheng Zhang, Yuhuai Chen, Yuming |
| description | In this paper, with eclipse stage in consideration, we propose an HIV-1 infection model with a general incidence rate and CTL immune response. We first study the existence and local stability of equilibria, which is characterized by the basic infection reproduction number
and the basic immunity reproduction number
. The local stability analysis indicates the occurrence of transcritical bifurcations of equilibria. We confirm the bifurcations at the disease-free equilibrium and the infected immune-free equilibrium with transmission rate and the decay rate of CTLs as bifurcation parameters, respectively. Then we apply the approach of Lyapunov functions to establish the global stability of the equilibria, which is determined by the two basic reproduction numbers. These theoretical results are supported with numerical simulations. Moreover, we also identify the high sensitivity parameters by carrying out the sensitivity analysis of the two basic reproduction numbers to the model parameters. |
| doi_str_mv | 10.1080/17513758.2021.1950224 |
| format | Article |
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and the basic immunity reproduction number
. The local stability analysis indicates the occurrence of transcritical bifurcations of equilibria. We confirm the bifurcations at the disease-free equilibrium and the infected immune-free equilibrium with transmission rate and the decay rate of CTLs as bifurcation parameters, respectively. Then we apply the approach of Lyapunov functions to establish the global stability of the equilibria, which is determined by the two basic reproduction numbers. These theoretical results are supported with numerical simulations. Moreover, we also identify the high sensitivity parameters by carrying out the sensitivity analysis of the two basic reproduction numbers to the model parameters.</description><identifier>ISSN: 1751-3758</identifier><identifier>EISSN: 1751-3766</identifier><identifier>DOI: 10.1080/17513758.2021.1950224</identifier><identifier>PMID: 34251981</identifier><language>eng</language><publisher>ABINGDON: Taylor & Francis</publisher><subject>Basic Reproduction Number ; bifurcation ; Computer Simulation ; Ecology ; Environmental Sciences & Ecology ; global stability ; HIV infection ; HIV-1 ; Immunity ; Incidence ; Life Sciences & Biomedicine ; Lyapunov function ; Mathematical & Computational Biology ; Models, Biological ; Science & Technology</subject><ispartof>Journal of biological dynamics, 2021-01, Vol.15 (1), p.367-394</ispartof><rights>2021 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group 2021</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>true</woscitedreferencessubscribed><woscitedreferencescount>4</woscitedreferencescount><woscitedreferencesoriginalsourcerecordid>wos000673052000001</woscitedreferencesoriginalsourcerecordid><citedby>FETCH-LOGICAL-c479t-cba9ebc254a8e7ffadebd3c21b19df5fbc493d4e631802820524c52d845545ee3</citedby><cites>FETCH-LOGICAL-c479t-cba9ebc254a8e7ffadebd3c21b19df5fbc493d4e631802820524c52d845545ee3</cites><orcidid>0000-0002-2896-5627</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.tandfonline.com/doi/pdf/10.1080/17513758.2021.1950224$$EPDF$$P50$$Ginformaworld$$Hfree_for_read</linktopdf><linktohtml>$$Uhttps://www.tandfonline.com/doi/full/10.1080/17513758.2021.1950224$$EHTML$$P50$$Ginformaworld$$Hfree_for_read</linktohtml><link.rule.ids>315,781,785,865,2103,2115,27506,27928,27929,59147,59148</link.rule.ids><backlink>$$Uhttps://www.ncbi.nlm.nih.gov/pubmed/34251981$$D View this record in MEDLINE/PubMed$$Hfree_for_read</backlink></links><search><creatorcontrib>Ma, Xinsheng</creatorcontrib><creatorcontrib>Zhang, Yuhuai</creatorcontrib><creatorcontrib>Chen, Yuming</creatorcontrib><title>Stability and bifurcation analysis of an HIV-1 infection model with a general incidence and CTL immune response</title><title>Journal of biological dynamics</title><addtitle>J BIOL DYNAM</addtitle><addtitle>J Biol Dyn</addtitle><description>In this paper, with eclipse stage in consideration, we propose an HIV-1 infection model with a general incidence rate and CTL immune response. We first study the existence and local stability of equilibria, which is characterized by the basic infection reproduction number
and the basic immunity reproduction number
. The local stability analysis indicates the occurrence of transcritical bifurcations of equilibria. We confirm the bifurcations at the disease-free equilibrium and the infected immune-free equilibrium with transmission rate and the decay rate of CTLs as bifurcation parameters, respectively. Then we apply the approach of Lyapunov functions to establish the global stability of the equilibria, which is determined by the two basic reproduction numbers. These theoretical results are supported with numerical simulations. Moreover, we also identify the high sensitivity parameters by carrying out the sensitivity analysis of the two basic reproduction numbers to the model parameters.</description><subject>Basic Reproduction Number</subject><subject>bifurcation</subject><subject>Computer Simulation</subject><subject>Ecology</subject><subject>Environmental Sciences & Ecology</subject><subject>global stability</subject><subject>HIV infection</subject><subject>HIV-1</subject><subject>Immunity</subject><subject>Incidence</subject><subject>Life Sciences & Biomedicine</subject><subject>Lyapunov function</subject><subject>Mathematical & Computational Biology</subject><subject>Models, Biological</subject><subject>Science & Technology</subject><issn>1751-3758</issn><issn>1751-3766</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><sourceid>0YH</sourceid><sourceid>HGBXW</sourceid><sourceid>EIF</sourceid><sourceid>DOA</sourceid><recordid>eNqNkU2P0zAQhiMEYj_gJ4ByREIp_kycGygCtlIlDixcLcceL145cbETVf33OE23xxW-eDzzvjPyPEXxDqMNRgJ9wg3HtOFiQxDBG9xyRAh7UVwv-Yo2df3yEnNxVdyk9IgQ56SpXxdXlBGOW4Gvi_BzUr3zbjqWajRl7-wctZpcGPNb-WNyqQw2x-Xd9neFSzda0KfyEAz48uCmP6UqH2CEqHwua2dg1HDq1t3vSjcM8whlhLQPY4I3xSurfIK35_u2-PXt6313V-1-fN92X3aVZk07VbpXLfSacKYENNYqA72hmuAet8Zy22vWUsOgplggIgjihGlOjGCcMw5Ab4vt2tcE9Sj30Q0qHmVQTp4SIT5IFSenPUjQuKHCCGHrhnFSC8C8p6wFYgkTrMm9Pqy99jH8nSFNcnBJg_dqhDAnSTjHBLW1YFnKV6mOIaUI9jIaI7lwk0_c5MJNnrll3_vziLkfwFxcT6CyQKyCA_TBJu2WJV9kCKG6oXkJaDm4c9MJYRfmccrWj_9vzerPqzqTDnFQhxC9kZM6-hBtVJlvkvT5z_wDvifHIQ</recordid><startdate>20210101</startdate><enddate>20210101</enddate><creator>Ma, Xinsheng</creator><creator>Zhang, Yuhuai</creator><creator>Chen, Yuming</creator><general>Taylor & Francis</general><general>Taylor & Francis Group</general><scope>0YH</scope><scope>BLEPL</scope><scope>DTL</scope><scope>HGBXW</scope><scope>CGR</scope><scope>CUY</scope><scope>CVF</scope><scope>ECM</scope><scope>EIF</scope><scope>NPM</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7X8</scope><scope>DOA</scope><orcidid>https://orcid.org/0000-0002-2896-5627</orcidid></search><sort><creationdate>20210101</creationdate><title>Stability and bifurcation analysis of an HIV-1 infection model with a general incidence and CTL immune response</title><author>Ma, Xinsheng ; Zhang, Yuhuai ; Chen, Yuming</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c479t-cba9ebc254a8e7ffadebd3c21b19df5fbc493d4e631802820524c52d845545ee3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Basic Reproduction Number</topic><topic>bifurcation</topic><topic>Computer Simulation</topic><topic>Ecology</topic><topic>Environmental Sciences & Ecology</topic><topic>global stability</topic><topic>HIV infection</topic><topic>HIV-1</topic><topic>Immunity</topic><topic>Incidence</topic><topic>Life Sciences & Biomedicine</topic><topic>Lyapunov function</topic><topic>Mathematical & Computational Biology</topic><topic>Models, Biological</topic><topic>Science & Technology</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Ma, Xinsheng</creatorcontrib><creatorcontrib>Zhang, Yuhuai</creatorcontrib><creatorcontrib>Chen, Yuming</creatorcontrib><collection>Access via Taylor & Francis (Open Access Collection)</collection><collection>Web of Science Core Collection</collection><collection>Science Citation Index Expanded</collection><collection>Web of Science - Science Citation Index Expanded - 2021</collection><collection>Medline</collection><collection>MEDLINE</collection><collection>MEDLINE (Ovid)</collection><collection>MEDLINE</collection><collection>MEDLINE</collection><collection>PubMed</collection><collection>CrossRef</collection><collection>MEDLINE - Academic</collection><collection>DOAJ Directory of Open Access Journals</collection><jtitle>Journal of biological dynamics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Ma, Xinsheng</au><au>Zhang, Yuhuai</au><au>Chen, Yuming</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Stability and bifurcation analysis of an HIV-1 infection model with a general incidence and CTL immune response</atitle><jtitle>Journal of biological dynamics</jtitle><stitle>J BIOL DYNAM</stitle><addtitle>J Biol Dyn</addtitle><date>2021-01-01</date><risdate>2021</risdate><volume>15</volume><issue>1</issue><spage>367</spage><epage>394</epage><pages>367-394</pages><issn>1751-3758</issn><eissn>1751-3766</eissn><abstract>In this paper, with eclipse stage in consideration, we propose an HIV-1 infection model with a general incidence rate and CTL immune response. We first study the existence and local stability of equilibria, which is characterized by the basic infection reproduction number
and the basic immunity reproduction number
. The local stability analysis indicates the occurrence of transcritical bifurcations of equilibria. We confirm the bifurcations at the disease-free equilibrium and the infected immune-free equilibrium with transmission rate and the decay rate of CTLs as bifurcation parameters, respectively. Then we apply the approach of Lyapunov functions to establish the global stability of the equilibria, which is determined by the two basic reproduction numbers. These theoretical results are supported with numerical simulations. Moreover, we also identify the high sensitivity parameters by carrying out the sensitivity analysis of the two basic reproduction numbers to the model parameters.</abstract><cop>ABINGDON</cop><pub>Taylor & Francis</pub><pmid>34251981</pmid><doi>10.1080/17513758.2021.1950224</doi><tpages>28</tpages><orcidid>https://orcid.org/0000-0002-2896-5627</orcidid><oa>free_for_read</oa></addata></record> |
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| subjects | Basic Reproduction Number bifurcation Computer Simulation Ecology Environmental Sciences & Ecology global stability HIV infection HIV-1 Immunity Incidence Life Sciences & Biomedicine Lyapunov function Mathematical & Computational Biology Models, Biological Science & Technology |
| title | Stability and bifurcation analysis of an HIV-1 infection model with a general incidence and CTL immune response |
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