Condition for Existence of Positive Periodic Solution of Hepatitis B Virus Infection Model with Immune Response

Min Long; Tiejun Zhou

doi:doi:10.11648/j.pamj.20130202.19

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Condition for Existence of Positive Periodic Solution of Hepatitis B Virus Infection Model with Immune Response

Min Long, Tiejun Zhou

Published in Pure and Applied Mathematics Journal (Volume 2, Issue 2)

Received: 21 April 2013 Accepted: Published: 30 May 2013

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Abstract

In this paper, we consider a periodic Hepatitis B Virus infection model with immune response. By using continuation theorem of coincidence degree theory, a condition for the existence of positive periodic solution is obtained

Published in	Pure and Applied Mathematics Journal (Volume 2, Issue 2)
DOI	10.11648/j.pamj.20130202.19
Page(s)	106-109
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Hepatitis B Virus Infection Model, Immune Response, Positive Periodic Solution, Coincidence Degree Theory

References

[1]	D. Lavanchy, "Hepatitis B virus epidemiology, disease burden, treatment, and current and emerging prevention and control measures," J. Viral Hepat, vol.11, pp. 97-107, Sept. 2004.
[2]	A.F. Lok, B.J. Mcmahon, "Chronic hepatitis B：Update 2009", Hepatology, vol. 50, pp.661-662, 2009．
[3]	A. Murase, T. Sasaki, T. Kajiwara, "Stability analysis of pathogen-immune interaction dynamics," J. Math. Biol., vol.51, pp. 247-267, Sept. 2005.
[4]	M. A. Nowak, C.R.M. Bangham, "Population Dynamics of Immune Responses to Persistent Viruses," Science, vol.272, pp.74-79, Apr. 1996.
[5]	S. M. Ciupe, R. M. Ribeiro, P. W. Nelson, A. S. Perelson, "Modeling the mechanisms of acute hepatitis B virus infection," J. Theor. Biol. vol.247, pp.23-35, Jul. 2007.
[6]	H. Fang, T. Zhou, "Analysis of an HBV infection dynamics model in immune response," Pure and Appl. Math., vol.28, pp.635-540, Oct. 2012.
[7]	Y. Ji, L. Min, Y. Zheng, Y. Su, "A viral infection model with periodic immune response and nonlinear CTL response," Math. Comp. Simul., vol. 80, pp. 2309- 2316, Aug.2010.
[8]	Q. Xie, D. Huang, S. Zhang, J. Cao, "Analysis of a viral infection model with delayed immune response," Appl. Math. Model. vol. 34, pp. 2388 - 2395, Sept. 2010.
[9]	A. Fan, K. Wang, "A viral infection model with immune circadian rhythms," Appl. Math. Comp., vol. 215, pp. 3369 - 3374, Jan. 2010.
[10]	R.Gaines, J.Mawhin. Coincidence Degree and Nonlinear Differential Equations, Springer -Verlag, Berlin, 1977.

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APA Style

Min Long, Tiejun Zhou. (2013). Condition for Existence of Positive Periodic Solution of Hepatitis B Virus Infection Model with Immune Response. Pure and Applied Mathematics Journal, 2(2), 106-109. https://doi.org/10.11648/j.pamj.20130202.19

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ACS Style

Min Long; Tiejun Zhou. Condition for Existence of Positive Periodic Solution of Hepatitis B Virus Infection Model with Immune Response. Pure Appl. Math. J. 2013, 2(2), 106-109. doi: 10.11648/j.pamj.20130202.19

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AMA Style

Min Long, Tiejun Zhou. Condition for Existence of Positive Periodic Solution of Hepatitis B Virus Infection Model with Immune Response. Pure Appl Math J. 2013;2(2):106-109. doi: 10.11648/j.pamj.20130202.19

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@article{10.11648/j.pamj.20130202.19,
  author = {Min Long and Tiejun Zhou},
  title = {Condition for Existence of Positive Periodic Solution of Hepatitis B Virus Infection Model with Immune Response},
  journal = {Pure and Applied Mathematics Journal},
  volume = {2},
  number = {2},
  pages = {106-109},
  doi = {10.11648/j.pamj.20130202.19},
  url = {https://doi.org/10.11648/j.pamj.20130202.19},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20130202.19},
  abstract = {In this paper, we consider a periodic Hepatitis B Virus infection model with immune response. By using continuation theorem of coincidence degree theory, a condition for the existence of positive periodic solution is obtained},
 year = {2013}
}

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TY  - JOUR
T1  - Condition for Existence of Positive Periodic Solution of Hepatitis B Virus Infection Model with Immune Response
AU  - Min Long
AU  - Tiejun Zhou
Y1  - 2013/05/30
PY  - 2013
N1  - https://doi.org/10.11648/j.pamj.20130202.19
DO  - 10.11648/j.pamj.20130202.19
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 106
EP  - 109
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20130202.19
AB  - In this paper, we consider a periodic Hepatitis B Virus infection model with immune response. By using continuation theorem of coincidence degree theory, a condition for the existence of positive periodic solution is obtained
VL  - 2
IS  - 2
ER  -

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Author Information

Min Long

College of Science, Hunan Agricultural University, Changsha, Hunan 410128, China
Tiejun Zhou

College of Science, Hunan Agricultural University, Changsha, Hunan 410129, China

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APA Style

Min Long, Tiejun Zhou. (2013). Condition for Existence of Positive Periodic Solution of Hepatitis B Virus Infection Model with Immune Response. Pure and Applied Mathematics Journal, 2(2), 106-109. https://doi.org/10.11648/j.pamj.20130202.19

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ACS Style

Min Long; Tiejun Zhou. Condition for Existence of Positive Periodic Solution of Hepatitis B Virus Infection Model with Immune Response. Pure Appl. Math. J. 2013, 2(2), 106-109. doi: 10.11648/j.pamj.20130202.19

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AMA Style

Min Long, Tiejun Zhou. Condition for Existence of Positive Periodic Solution of Hepatitis B Virus Infection Model with Immune Response. Pure Appl Math J. 2013;2(2):106-109. doi: 10.11648/j.pamj.20130202.19

Copy | Download

@article{10.11648/j.pamj.20130202.19,
  author = {Min Long and Tiejun Zhou},
  title = {Condition for Existence of Positive Periodic Solution of Hepatitis B Virus Infection Model with Immune Response},
  journal = {Pure and Applied Mathematics Journal},
  volume = {2},
  number = {2},
  pages = {106-109},
  doi = {10.11648/j.pamj.20130202.19},
  url = {https://doi.org/10.11648/j.pamj.20130202.19},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20130202.19},
  abstract = {In this paper, we consider a periodic Hepatitis B Virus infection model with immune response. By using continuation theorem of coincidence degree theory, a condition for the existence of positive periodic solution is obtained},
 year = {2013}
}

Copy | Download

TY  - JOUR
T1  - Condition for Existence of Positive Periodic Solution of Hepatitis B Virus Infection Model with Immune Response
AU  - Min Long
AU  - Tiejun Zhou
Y1  - 2013/05/30
PY  - 2013
N1  - https://doi.org/10.11648/j.pamj.20130202.19
DO  - 10.11648/j.pamj.20130202.19
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 106
EP  - 109
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20130202.19
AB  - In this paper, we consider a periodic Hepatitis B Virus infection model with immune response. By using continuation theorem of coincidence degree theory, a condition for the existence of positive periodic solution is obtained
VL  - 2
IS  - 2
ER  -

Copy | Download