Global stability of a delay differential equation of hepatitis B virus infection with immune response

The global stability for a delayed HBV infection model with CTL immune response is investigated. We show that the global dynamics is determined by two sharp thresholds, basic reproduction number $Re_0$ and CTL immune-response reproduction number $Re_1$. When $Re_0 leq 1$, the infection-free equi...
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Gespeichert in:

Autor*in:	Jinliang Wang [verfasserIn] Xinxin Tian [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2013

Schlagwörter:	HBV infection model delay CTLs global stability

Übergeordnetes Werk:	In: Electronic Journal of Differential Equations - Texas State University, 2003, (2013), 94,, Seite 11
Übergeordnetes Werk:	year:2013 ; number:94, ; pages:11

Links:	Link aufrufen Link aufrufen Journal toc

Katalog-ID:	DOAJ021905460

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520			\|a The global stability for a delayed HBV infection model with CTL immune response is investigated. We show that the global dynamics is determined by two sharp thresholds, basic reproduction number $Re_0$ and CTL immune-response reproduction number $Re_1$. When $Re_0 leq 1$, the infection-free equilibrium is globally asymptotically stable, which means that the viruses are cleared and immune is not active; when $Re_1 leq 1 < Re_0$, the CTL-inactivated infection equilibrium exists and is globally asymptotically stable, which means that CTLs immune response would not be activated and viral infection becomes chronic; and when $Re_1 < 1$, the CTL-activated infection equilibrium exists and is globally asymptotically stable, in this case the infection causes a persistent CTLs immune response. Our model is formulated by incorporating a Cytotoxic T lymphocytes (CTLs) immune response to recent work [Gourley, Kuang, Nagy, J. Bio. Dyn., 2(2008), 140-153] to model the role in antiviral by attacking virus infected cells. Our analysis provides a quantitative understandings of HBV replication dynamics in vivo and has implications for the optimal timing of drug treatment and immunotherapy in chronic HBV infection.
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allfields	(DE-627)DOAJ021905460 (DE-599)DOAJ6651632806d04d409afaaf7221479c9c DE-627 ger DE-627 rakwb eng QA1-939 Jinliang Wang verfasserin aut Global stability of a delay differential equation of hepatitis B virus infection with immune response 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The global stability for a delayed HBV infection model with CTL immune response is investigated. We show that the global dynamics is determined by two sharp thresholds, basic reproduction number $Re_0$ and CTL immune-response reproduction number $Re_1$. When $Re_0 leq 1$, the infection-free equilibrium is globally asymptotically stable, which means that the viruses are cleared and immune is not active; when $Re_1 leq 1 < Re_0$, the CTL-inactivated infection equilibrium exists and is globally asymptotically stable, which means that CTLs immune response would not be activated and viral infection becomes chronic; and when $Re_1 < 1$, the CTL-activated infection equilibrium exists and is globally asymptotically stable, in this case the infection causes a persistent CTLs immune response. Our model is formulated by incorporating a Cytotoxic T lymphocytes (CTLs) immune response to recent work [Gourley, Kuang, Nagy, J. Bio. Dyn., 2(2008), 140-153] to model the role in antiviral by attacking virus infected cells. Our analysis provides a quantitative understandings of HBV replication dynamics in vivo and has implications for the optimal timing of drug treatment and immunotherapy in chronic HBV infection. HBV infection model delay CTLs global stability Mathematics Xinxin Tian verfasserin aut In Electronic Journal of Differential Equations Texas State University, 2003 (2013), 94,, Seite 11 (DE-627)320518205 (DE-600)2014226-2 10726691 nnns year:2013 number:94, pages:11 https://doaj.org/article/6651632806d04d409afaaf7221479c9c kostenfrei http://ejde.math.txstate.edu/Volumes/2013/94/abstr.html kostenfrei https://doaj.org/toc/1072-6691 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ SSG-OLC-PHA GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2031 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2061 GBV_ILN_2111 GBV_ILN_2190 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2013 94, 11
spelling	(DE-627)DOAJ021905460 (DE-599)DOAJ6651632806d04d409afaaf7221479c9c DE-627 ger DE-627 rakwb eng QA1-939 Jinliang Wang verfasserin aut Global stability of a delay differential equation of hepatitis B virus infection with immune response 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The global stability for a delayed HBV infection model with CTL immune response is investigated. We show that the global dynamics is determined by two sharp thresholds, basic reproduction number $Re_0$ and CTL immune-response reproduction number $Re_1$. When $Re_0 leq 1$, the infection-free equilibrium is globally asymptotically stable, which means that the viruses are cleared and immune is not active; when $Re_1 leq 1 < Re_0$, the CTL-inactivated infection equilibrium exists and is globally asymptotically stable, which means that CTLs immune response would not be activated and viral infection becomes chronic; and when $Re_1 < 1$, the CTL-activated infection equilibrium exists and is globally asymptotically stable, in this case the infection causes a persistent CTLs immune response. Our model is formulated by incorporating a Cytotoxic T lymphocytes (CTLs) immune response to recent work [Gourley, Kuang, Nagy, J. Bio. Dyn., 2(2008), 140-153] to model the role in antiviral by attacking virus infected cells. Our analysis provides a quantitative understandings of HBV replication dynamics in vivo and has implications for the optimal timing of drug treatment and immunotherapy in chronic HBV infection. HBV infection model delay CTLs global stability Mathematics Xinxin Tian verfasserin aut In Electronic Journal of Differential Equations Texas State University, 2003 (2013), 94,, Seite 11 (DE-627)320518205 (DE-600)2014226-2 10726691 nnns year:2013 number:94, pages:11 https://doaj.org/article/6651632806d04d409afaaf7221479c9c kostenfrei http://ejde.math.txstate.edu/Volumes/2013/94/abstr.html kostenfrei https://doaj.org/toc/1072-6691 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ SSG-OLC-PHA GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2031 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2061 GBV_ILN_2111 GBV_ILN_2190 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2013 94, 11
allfields_unstemmed	(DE-627)DOAJ021905460 (DE-599)DOAJ6651632806d04d409afaaf7221479c9c DE-627 ger DE-627 rakwb eng QA1-939 Jinliang Wang verfasserin aut Global stability of a delay differential equation of hepatitis B virus infection with immune response 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The global stability for a delayed HBV infection model with CTL immune response is investigated. We show that the global dynamics is determined by two sharp thresholds, basic reproduction number $Re_0$ and CTL immune-response reproduction number $Re_1$. When $Re_0 leq 1$, the infection-free equilibrium is globally asymptotically stable, which means that the viruses are cleared and immune is not active; when $Re_1 leq 1 < Re_0$, the CTL-inactivated infection equilibrium exists and is globally asymptotically stable, which means that CTLs immune response would not be activated and viral infection becomes chronic; and when $Re_1 < 1$, the CTL-activated infection equilibrium exists and is globally asymptotically stable, in this case the infection causes a persistent CTLs immune response. Our model is formulated by incorporating a Cytotoxic T lymphocytes (CTLs) immune response to recent work [Gourley, Kuang, Nagy, J. Bio. Dyn., 2(2008), 140-153] to model the role in antiviral by attacking virus infected cells. Our analysis provides a quantitative understandings of HBV replication dynamics in vivo and has implications for the optimal timing of drug treatment and immunotherapy in chronic HBV infection. HBV infection model delay CTLs global stability Mathematics Xinxin Tian verfasserin aut In Electronic Journal of Differential Equations Texas State University, 2003 (2013), 94,, Seite 11 (DE-627)320518205 (DE-600)2014226-2 10726691 nnns year:2013 number:94, pages:11 https://doaj.org/article/6651632806d04d409afaaf7221479c9c kostenfrei http://ejde.math.txstate.edu/Volumes/2013/94/abstr.html kostenfrei https://doaj.org/toc/1072-6691 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ SSG-OLC-PHA GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2031 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2061 GBV_ILN_2111 GBV_ILN_2190 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2013 94, 11
allfieldsGer	(DE-627)DOAJ021905460 (DE-599)DOAJ6651632806d04d409afaaf7221479c9c DE-627 ger DE-627 rakwb eng QA1-939 Jinliang Wang verfasserin aut Global stability of a delay differential equation of hepatitis B virus infection with immune response 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The global stability for a delayed HBV infection model with CTL immune response is investigated. We show that the global dynamics is determined by two sharp thresholds, basic reproduction number $Re_0$ and CTL immune-response reproduction number $Re_1$. When $Re_0 leq 1$, the infection-free equilibrium is globally asymptotically stable, which means that the viruses are cleared and immune is not active; when $Re_1 leq 1 < Re_0$, the CTL-inactivated infection equilibrium exists and is globally asymptotically stable, which means that CTLs immune response would not be activated and viral infection becomes chronic; and when $Re_1 < 1$, the CTL-activated infection equilibrium exists and is globally asymptotically stable, in this case the infection causes a persistent CTLs immune response. Our model is formulated by incorporating a Cytotoxic T lymphocytes (CTLs) immune response to recent work [Gourley, Kuang, Nagy, J. Bio. Dyn., 2(2008), 140-153] to model the role in antiviral by attacking virus infected cells. Our analysis provides a quantitative understandings of HBV replication dynamics in vivo and has implications for the optimal timing of drug treatment and immunotherapy in chronic HBV infection. HBV infection model delay CTLs global stability Mathematics Xinxin Tian verfasserin aut In Electronic Journal of Differential Equations Texas State University, 2003 (2013), 94,, Seite 11 (DE-627)320518205 (DE-600)2014226-2 10726691 nnns year:2013 number:94, pages:11 https://doaj.org/article/6651632806d04d409afaaf7221479c9c kostenfrei http://ejde.math.txstate.edu/Volumes/2013/94/abstr.html kostenfrei https://doaj.org/toc/1072-6691 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ SSG-OLC-PHA GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2031 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2061 GBV_ILN_2111 GBV_ILN_2190 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2013 94, 11
allfieldsSound	(DE-627)DOAJ021905460 (DE-599)DOAJ6651632806d04d409afaaf7221479c9c DE-627 ger DE-627 rakwb eng QA1-939 Jinliang Wang verfasserin aut Global stability of a delay differential equation of hepatitis B virus infection with immune response 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The global stability for a delayed HBV infection model with CTL immune response is investigated. We show that the global dynamics is determined by two sharp thresholds, basic reproduction number $Re_0$ and CTL immune-response reproduction number $Re_1$. When $Re_0 leq 1$, the infection-free equilibrium is globally asymptotically stable, which means that the viruses are cleared and immune is not active; when $Re_1 leq 1 < Re_0$, the CTL-inactivated infection equilibrium exists and is globally asymptotically stable, which means that CTLs immune response would not be activated and viral infection becomes chronic; and when $Re_1 < 1$, the CTL-activated infection equilibrium exists and is globally asymptotically stable, in this case the infection causes a persistent CTLs immune response. Our model is formulated by incorporating a Cytotoxic T lymphocytes (CTLs) immune response to recent work [Gourley, Kuang, Nagy, J. Bio. Dyn., 2(2008), 140-153] to model the role in antiviral by attacking virus infected cells. Our analysis provides a quantitative understandings of HBV replication dynamics in vivo and has implications for the optimal timing of drug treatment and immunotherapy in chronic HBV infection. HBV infection model delay CTLs global stability Mathematics Xinxin Tian verfasserin aut In Electronic Journal of Differential Equations Texas State University, 2003 (2013), 94,, Seite 11 (DE-627)320518205 (DE-600)2014226-2 10726691 nnns year:2013 number:94, pages:11 https://doaj.org/article/6651632806d04d409afaaf7221479c9c kostenfrei http://ejde.math.txstate.edu/Volumes/2013/94/abstr.html kostenfrei https://doaj.org/toc/1072-6691 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ SSG-OLC-PHA GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2031 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2061 GBV_ILN_2111 GBV_ILN_2190 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2013 94, 11
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callnumber-first	Q - Science
author	Jinliang Wang
spellingShingle	Jinliang Wang misc QA1-939 misc HBV infection model misc delay misc CTLs misc global stability misc Mathematics Global stability of a delay differential equation of hepatitis B virus infection with immune response
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topic_title	QA1-939 Global stability of a delay differential equation of hepatitis B virus infection with immune response HBV infection model delay CTLs global stability
topic	misc QA1-939 misc HBV infection model misc delay misc CTLs misc global stability misc Mathematics
topic_unstemmed	misc QA1-939 misc HBV infection model misc delay misc CTLs misc global stability misc Mathematics
topic_browse	misc QA1-939 misc HBV infection model misc delay misc CTLs misc global stability misc Mathematics
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title	Global stability of a delay differential equation of hepatitis B virus infection with immune response
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title_full	Global stability of a delay differential equation of hepatitis B virus infection with immune response
author_sort	Jinliang Wang
journal	Electronic Journal of Differential Equations
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author_browse	Jinliang Wang Xinxin Tian
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title_sort	global stability of a delay differential equation of hepatitis b virus infection with immune response
callnumber	QA1-939
title_auth	Global stability of a delay differential equation of hepatitis B virus infection with immune response
abstract	The global stability for a delayed HBV infection model with CTL immune response is investigated. We show that the global dynamics is determined by two sharp thresholds, basic reproduction number $Re_0$ and CTL immune-response reproduction number $Re_1$. When $Re_0 leq 1$, the infection-free equilibrium is globally asymptotically stable, which means that the viruses are cleared and immune is not active; when $Re_1 leq 1 < Re_0$, the CTL-inactivated infection equilibrium exists and is globally asymptotically stable, which means that CTLs immune response would not be activated and viral infection becomes chronic; and when $Re_1 < 1$, the CTL-activated infection equilibrium exists and is globally asymptotically stable, in this case the infection causes a persistent CTLs immune response. Our model is formulated by incorporating a Cytotoxic T lymphocytes (CTLs) immune response to recent work [Gourley, Kuang, Nagy, J. Bio. Dyn., 2(2008), 140-153] to model the role in antiviral by attacking virus infected cells. Our analysis provides a quantitative understandings of HBV replication dynamics in vivo and has implications for the optimal timing of drug treatment and immunotherapy in chronic HBV infection.
abstractGer	The global stability for a delayed HBV infection model with CTL immune response is investigated. We show that the global dynamics is determined by two sharp thresholds, basic reproduction number $Re_0$ and CTL immune-response reproduction number $Re_1$. When $Re_0 leq 1$, the infection-free equilibrium is globally asymptotically stable, which means that the viruses are cleared and immune is not active; when $Re_1 leq 1 < Re_0$, the CTL-inactivated infection equilibrium exists and is globally asymptotically stable, which means that CTLs immune response would not be activated and viral infection becomes chronic; and when $Re_1 < 1$, the CTL-activated infection equilibrium exists and is globally asymptotically stable, in this case the infection causes a persistent CTLs immune response. Our model is formulated by incorporating a Cytotoxic T lymphocytes (CTLs) immune response to recent work [Gourley, Kuang, Nagy, J. Bio. Dyn., 2(2008), 140-153] to model the role in antiviral by attacking virus infected cells. Our analysis provides a quantitative understandings of HBV replication dynamics in vivo and has implications for the optimal timing of drug treatment and immunotherapy in chronic HBV infection.
abstract_unstemmed	The global stability for a delayed HBV infection model with CTL immune response is investigated. We show that the global dynamics is determined by two sharp thresholds, basic reproduction number $Re_0$ and CTL immune-response reproduction number $Re_1$. When $Re_0 leq 1$, the infection-free equilibrium is globally asymptotically stable, which means that the viruses are cleared and immune is not active; when $Re_1 leq 1 < Re_0$, the CTL-inactivated infection equilibrium exists and is globally asymptotically stable, which means that CTLs immune response would not be activated and viral infection becomes chronic; and when $Re_1 < 1$, the CTL-activated infection equilibrium exists and is globally asymptotically stable, in this case the infection causes a persistent CTLs immune response. Our model is formulated by incorporating a Cytotoxic T lymphocytes (CTLs) immune response to recent work [Gourley, Kuang, Nagy, J. Bio. Dyn., 2(2008), 140-153] to model the role in antiviral by attacking virus infected cells. Our analysis provides a quantitative understandings of HBV replication dynamics in vivo and has implications for the optimal timing of drug treatment and immunotherapy in chronic HBV infection.
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container_issue	94,
title_short	Global stability of a delay differential equation of hepatitis B virus infection with immune response
url	https://doaj.org/article/6651632806d04d409afaaf7221479c9c http://ejde.math.txstate.edu/Volumes/2013/94/abstr.html https://doaj.org/toc/1072-6691
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up_date	2024-07-03T23:21:02.128Z
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