Hepatitis B virus infection model with vertical transmission and infection period

doi:10.3969/j.issn.1000-1565.2017.06.002

Abstract

Abstract: Hepatitis B virus infection model with vertical transmission and infection period were studied.By consider the epidemic models with nonlinear incidence rate,making infection period as time delay,and making use of Routh-Hurwite criterion to prove that condition of disease-free equilibrium is local asymptotic stability,we obtained a basic reproductive number R₀ and proved the global asymptotic stability of endemic equilibrium by using the Lyapunov functional method.

Key words: HBV epidemic model, time delay, global asymptotic stability, nonlinear incidence rate, vertical transmission

CLC Number:

O175

TAO Yujie,FENG Heping. Hepatitis B virus infection model with vertical transmission and infection period[J]. Journal of Hebei University (Natural Science Edition), 2017, 37(6): 567-571.

References

[1] JIA J D.Hepatitis B in China: from guideline to practice[J].Virol Sin,2008,23:152-155.DOI:10.1007/s12250-008-2953-8.
[2] LU F,ZHUANG H.Management of hepatitis B in China[J].Chinese Medical Journal,2009,122: 3-4.DOI:10.3760/cma.j.issn.0366-6999.2009.01.001.
[3] ALEXANDER M E,MOGHADAS S M.Periodicity in an epidemic model with ageneralized non-linear incidence[J].Mathematical Biosciences,189(1): 75-96.DOI:10.1016/j.mbs.2004.01.003.
[4] 张冉.具有类年龄结构的传染病模型的全局性态分析[D].哈尔滨:黑龙江大学,2015. ZHANG R.Global behavior analysis of epidemic model with age - like structure[D].Haerbin:Heilongjiang University,2015.
[5] THORNLEY S,BULLEN C,ROBERTS M.Hepatitis B in a high prevalence New Zealand population: A mathematical model applied to infection control policy[J].Journal of Theoretical Biology,2008,254(3): 599-603.DOI:10.1016/j.jtbi.2008.06.022.
[6] MEDLEY G F,LINDOP N A,EDMUNDS W J.Hepatitis-B virus endemicity: heterogeneity,catastrophic dynamics and control[J].Nature Medicine,2001,7(5): 619-624.DOI:10.1038/87953.
[7] 宋运娜.具有脉冲接种、垂直传染的SEIRS 乙肝数学模型[J].复旦学报(自然科学版),2015,54(3):308-312. SONG Y N.A mathematical model of SEIRS hepatitis B with pulsed and vertical infection[J].Journal of Fudan University(Natural Science Edition),2015,54(3):308-312.
[8] ZOU L,ZHANG W,RUAN S.Modeling the transmission dynamics and control of hepatitis B virus in China[J].Journal of Theoretical Biology,2010,262(2): 330-338.DOI:10.1016/j.jtbi.2009.09.035.
[9] PANG J,CUI J,ZHOU X.Dynamical behavior of a hepatitis B virus transmission model with vaccination[J].Journal of Theoretical Biology,2010,265(4):572-578.DOI:10.1016/j.jtbi.2010.05.038.
[10] WANG K,WANG W,SONG S.Dynamics of an HBV model with diffusion and delay[J].Journal of Theoretical Biology,2008,253(1): 36-44.DOI:10.1016/j.jtbi.2007.11.007.
[11] XU R,MA Z.An HBV model with diffusion and time delay[J].Journal of Theoretical Biology,2009,257(3): 499-509.DOI:10.1016/j.jtbi.2009.01.001.
[12] DING P,QIU Z,LI X.The population-level impact of HBV and its vaccination on HIV transmission dynamics[J].Mathematical Methods in the Applied Sciences,2016,39(18):5539-5556.DOI:10.1002/mma.3941.
[13] LIU S J,ZHU Q.HBV disabusing and answering doubt[M].Beijing: Chinese Medicine and Scientific Technology Publishing Company,2003.
[14] New Zealand Ministry of Health.Immunisation Handbook 2006[M].[S.l.] Wellington Ministry of Health,2006.
[15] PEI Y,LI S,LI C,et al.The effect of constant and pulse vaccination on an SIR epidemic model with infectious period[J].Applied Mathematical Modeling,35(8): 3866-3878.DOI:10.1016/j.apm.2011.02.012 Cite this publication.