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The analysis and application of an HBV model. (English) Zbl 1243.34054
Summary: A mathematical model is formulated to describe the spread of hepatitis B. The stability of equilibria and persistence of disease are analyzed. The results shows that the dynamics of the model is completely determined by the basic reproductive number ρ 0 . If ρ 0 <1, the disease-free equilibrium is globally stable. When ρ 0 >1, the disease-free equilibrium is unstable and the disease is uniformly persistent. Furthermore, under certain conditions, it is proved that the endemic equilibrium is globally attractive. Numerical simulations are conducted to demonstrate our theoretical results. The model is applied to HBV transmission in China. The parameter values of the model are estimated based on available HBV epidemic data in China. The simulation results matches the HBV epidemic data in China approximately.
34C20Transformation and reduction of ODE and systems, normal forms
34C60Qualitative investigation and simulation of models (ODE)
[1]World Health Organization. 2008, hepatitis B. World Health Organization Fact Sheet Nnbsp; 204. lt;http://www.who.int/mediacentre/factsheets/fs204/en/index.htmlgt;.
[2]Seeger, C.; Mason, W.: Hepatitis B virus biology, Microbiol. mol. Biol. rev. 64, 51-68 (2000)
[3]Candotti, D.; Opare-Sem, O.; Rezvan, H.; Sarkodie, F.; Allain, J. P.: Molecular and serological characterization of hepatitis B virus in deferred ghanaian blood donors with and without elevated alanine aminotransferase, J. viral. Hepat. 13, 715-724 (2006)
[4]Kane, M.: Global programme for control of hepatitis B infection, Vaccine 13, S47-S49 (1995)
[5]Chinese Center for Disease Control and Prevention. lt;http://www.chinacdc.cn/n272442/n272530/n3479265/n3479303/37095.htmlgt;.
[6]Medley, G. F.; Lindop, N. A.; Edmunds, W. J.; Nokes, D. James: Hepatitis-B virus endemicity: heterogeneity, catastrophic dynamics and control, Nat. med. 7, 619-624 (2001)
[7]Ministry of Health of the People’s Republic of China. National report of notifiable diseases, 2004-2009. lt;http://www.moh.gov.cn/publicfiles//business/htmlfiles/wsb/pyqxx/list.htmgt;.
[8]Hou, J. L.; Liu, Z. H.; Gu, F.: Epidemiology and prevention of hepatitis B virus infection, Int. J. Med. sci. 2, 50-57 (2005)
[9]Wang, Z.; Zhang, J.; Yang, H.: Quantitative analysis of HBV DNA level and hbeag titer in hepatitis B surface antigen positive mothers and their babies: hbeag passage through the placenta and the rate of decay in babies, J. med. Virol. 71, 360-366 (2003)
[10]Xu, D.; Yan, Y.; Choi, B. C.: Risk factors and mechanism of transplacental transmission of hepatitis B virus: a case control study, J. med. Virol. 67, 20-26 (2002)
[11]John, T. J.; Cooksley, G.: Hepatitis B vaccine boosters: is there a clinical need in high endemicity populations, J. gastroenterol. Hepatol. 20, 5-10 (2005)
[12]O’leary, C.; Hong, Z.; Zhang, F.; Dawood, M.; Smart, G.; Kaita, K.; Wu, J.: A mathematical model to study the effect of hepatitis B virus vaccine and antivirus treatment among the canadian inuit population, Eur. J. Clin. microbiol. Infect. dis. 29, 63-72 (2010)
[13]Zou, L.; Zhang, W. N.; Ruan, S. G.: Modeling the transmission dynamics and control of hepatitis B virus in China, J. theor. Biol. 262, 330-338 (2010)
[14]Thornley, S.; Bullen, C.; Roberts, M.: Hepatitis B in a high prevalence New Zealand population: a mathematical model applied to infection control policy, J. theor. Biol. 254, 599-603 (2008)
[15]Hahne’, S.; Ramsay, M.; Balogum, K.: Incidence and routes of transmission of hepatitis B virus in england and wales, 1995 – 2000: implications for immunisation policy, J. clin. Virol. 29, 211-220 (2004)
[16]Mclean, A. R.; Blumberg, B. S.: Modelling the impact of mass vaccination against hepatitis B.I. Model formulation and parameter estimation, Proc. R. Soc. lond. B. 256, 7-15 (1994)
[17]Zhao, S. J.; Xu, Z. Y.; Lu, Y.: A mathematical model of hepatitis B virus transmission and its application for vaccination strategy in China, Int. J. Epidemiol. 29, 744-752 (2000)
[18]Hoofnagle, J. H.; Doo, E.; Liang, T. J.; Fleischer, R.; Lok, A. S.: Management of hepatitis B: summary of a clinical research workshop, Hepatology 45, 1056-1075 (2007)
[19]Hyams, K. C.: Risks of chronicity following acute hepatitis B virus infection: a review, Clin. infect. Dis. 20, 992-1000 (1995)
[20]Den Driessche, P. Van; Watmough, J.: Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. biosci. 180, 29-48 (2002) · Zbl 1015.92036 · doi:10.1016/S0025-5564(02)00108-6
[21]Lasalle, J. P.: The stability of dynamical systems, regional conference series in applied mathematics, (1976)
[22]Smith, H. L.: Monotone dynamical systems: an introduction to the theory of competitive and cooperative systems, mathematical surveys and monographs, Amer. math. Soc. prov. 41 (1995) · Zbl 0821.34003
[23]Zhao, X. Q.: Dynamical systems in population biology, (2003)
[24]Jia, J. D.: Hepatitis B in China: from guideline to practice, Virol. sin. 23, 152-155 (2008)
[25]National Bureau of Statistics of China. China Statistical Yearbook 2009, Birth rate, Death rate and Natural growth rate of population.lt;ttp://www.stats.gov.cn/tjsj/ndsj/2009/indexch.htmgt;.
[26]Edmunds, W. J.; Medley, G. F.; Nokes, D. J.: The transmission dynamics and control of hepatitis B virus in the gambia, Stat. med. 15, 2215-2233 (1996)