Dynamic analysis of a hepatitis B model with three-age-classes

Abstract Based on the fact that the likelihood of becoming chronically infected is dependent on age at primary infection Kane (1995) [2], Edmunds et al. (1993) [3], Medley et al. (2001) [4], and Ganem and Prince (2004) [6], we formulate a hepatitis B transmission model with three age classes. The reproduction number, R 0 is defined and the dynamical behavior of the model is analyzed. It is proved that the disease-free equilibrium is globally stable if R 0 1 , and there exists at least one endemic equilibrium and that the disease is uniformly persistent if R 0 > 1 . The unique endemic equilibrium and its global stability is obtained in a special case. Simulations are also conducted to compare the dynamical behavior of the model with and without age classes.

[1]  G. Fattovich.  Natural history of hepatitis B. , 2003, Journal of hepatology.

[2]  Xiao-Qiang Zhao,et al.  Dynamical systems in population biology , 2003 .

[3]  Z Xu,et al.  A mathematical model of hepatitis B virus transmission and its application for vaccination strategy in china. , 2000, International journal of epidemiology.

[4]  T. John,et al.  Hepatitis B vaccine boosters: Is there a clinical need in high endemicity populations? , 2005, Journal of gastroenterology and hepatology.

[5]  A J Hall,et al.  The influence of age on the development of the hepatitis B carrier state , 1993, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[6]  Lan Zou,et al.  Modeling the transmission dynamics and control of hepatitis B virus in China. , 2010, Journal of theoretical biology.

[7]  Hal L. Smith,et al.  Monotone Dynamical Systems: An Introduction To The Theory Of Competitive And Cooperative Systems (Mathematical Surveys And Monographs) By Hal L. Smith , 1995 .

[8]  C. Seeger,et al.  Hepatitis B Virus Biology , 2000, Microbiology and Molecular Biology Reviews.

[9]  Graham F. Medley,et al.  Hepatitis-B virus endemicity: heterogeneity, catastrophic dynamics and control , 2001, Nature Medicine.

[10]  K. Hyams.  Risks of chronicity following acute hepatitis B virus infection: a review. , 1995, Clinical infectious diseases : an official publication of the Infectious Diseases Society of America.

[11]  C. Bullen,et al.  Hepatitis B in a high prevalence New Zealand population: a mathematical model applied to infection control policy. , 2008, Journal of theoretical biology.

[12]  J. Watmough,et al.  Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. , 2002, Mathematical biosciences.

[13]  Mick Roberts,et al.  Modelling the epidemiology of hepatitis B in New Zealand. , 2011, Journal of theoretical biology.

[14]  M. Kane.  Epidemiology of hepatitis B infection in North America. , 1995, Vaccine.

[15]  R. May,et al.  Infectious Diseases of Humans: Dynamics and Control , 1991, Annals of Internal Medicine.

[16]  Jianhua Pang,et al.  Dynamical behavior of a hepatitis B virus transmission model with vaccination. , 2010, Journal of theoretical biology.

[17]  D. Ganem,et al.  Hepatitis B virus infection--natural history and clinical consequences. , 2004, The New England journal of medicine.

[18]  N. Gitlin.  Hepatitis B: diagnosis, prevention, and treatment. , 1997, Clinical chemistry.

[19]  J. Hoofnagle,et al.  Management of hepatitis B: Summary of a clinical research workshop , 2007, Hepatology.