The transmission dynamic and optimal control of acute and chronic hepatitis B

References

• R.M. Anderson and R.M. May, Infectious Disease of Humans, Dynamics and Control, Oxford University Press, Oxford, 1991.
   Google Scholar
• G. Birkhoff and G.C. Rota, Ordinary Differential Equation, 4th ed., John Wiley and Sons, New York, NY, 1989.
   Google Scholar
• M.H. Chang, Hepatitis virus infection, Semin. Fetal Neonatal Med. 12 (2007), pp. 160–167. doi: 10.1016/j.siny.2007.01.013
   Google Scholar
• CDC, Public Health Service inter-agency guidelines for screening donors of blood, plasma, organs, tissues, and semen for evidence of hepatitis B and hepatitis C, MMWR 40 (1991), pp. 1–17.
   Google Scholar
• I.K. Dontwi, W. Obeng-Denteh, L. Obin-Apraku and E.A. Andam, Modeling hepatitis B in a high prevalence district Ghana, Br. J. Math. Comput. Sci. 4 (2014), pp. 969–988. doi: 10.9734/BJMCS/2014/4682
   Google Scholar
• V.D. Driessche and P. Watmough, Reproduction numbers and sub threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci. 180 (2002), pp. 29–48. doi: 10.1016/S0025-5564(02)00108-6
   Google Scholar
• A.V. Kamyad, R. Akbari, A.A. Heydari, and A. Heydari, Mathematical modeling of transmission dynamics and optimal control of vaccination and treatment for hepatitis B virus, Comput. Math. Methods Med. 475451 (2014), pp. 1–15. doi: 10.1155/2014/475451
   Google Scholar
• T. Khan, G. Zaman, and O. Algahtani, Transmission dynamic and vaccination of hepatitis B epidemic model, WULFENIA J. 22 (2015), pp. 230–241.
   Google Scholar
• J.P. LaSalle, The Stability of Dynamical Systems, SIAM, Philadelphia, PA, 1976.
   Google Scholar
• D. Lavanchy, Hepatitis B virus epidemiology, disease burden, treatment, and current and emerging prevention and control measures, J. Viral Hepat. 11 (2004), pp. 97–107. doi: 10.1046/j.1365-2893.2003.00487.x
   Google Scholar
• M.K. Libbus and L.M. phillips, Public health management of perinatal hepatitis B virus, Public Health Nurs. 26 (2009), pp. 353–361. doi: 10.1111/j.1525-1446.2009.00790.x
   Google Scholar
• A.S. Lok, E.J Heathcote, and J.H. Hoofnagle, Management of hepatitis B, 2000 – Summary of a workshop, Gastroenterology 120 (2001), pp. 1828–1853. doi: 10.1053/gast.2001.24839
   Google Scholar
• J. Mann and M. Roberts, Modelling the epidemiology of hepatitis B in New Zealand, J. Theor. Biol. 269 (2011), pp. 266–272. doi: 10.1016/j.jtbi.2010.10.028
   Google Scholar
• J.E. Maynard, M.A. Kane, and S.C. Hadler, Global control of hepatitis B through vaccination role of hepatitis B vaccine in the expanded programme on immunization, Rev. Infect. 2 (1989), pp. S574–S578. doi: 10.1093/clinids/11.Supplement_3.S574
   Google Scholar
• B.J. McMahon, Epidemiology and natural history of hepatitis B, Semin. Liver Dis. 25 (2005), pp. 3–8. doi: 10.1055/s-2005-915644
   Google Scholar
• G.F. Medley, N.A. Lindop, W.J. Edmunds, and D.J. Nokes, Hepatitis-B virus endemicity, heterogeneity, catastrophic dynamics and control, Nat. Med. 7 (2001), pp. 619–624. doi: 10.1038/87953
   Google Scholar
• J.R. Nokes, D.J. Medley, and G.F. Anderson, The transmission dynamics of hepatitis B in the UK: A mathematical model for evaluating costs and effectiveness of immunization programmes, Epidemiol. Infect. 116 (1996), pp. 71–89. doi: 10.1017/S0950268800058970
   Google Scholar
• J. Pang, J.-A. Cui, and X. Zhou, Dynamical behavior of a hepatitis B virus transmission model with vaccination, J. Theor. Biol. 265 (2010), pp. 572–578. doi: 10.1016/j.jtbi.2010.05.038
   Google Scholar
• C.W. Shepard, E.P. Simard, L. Finelli, A.E. Fiore, and B.P. Bell, Hepatitis B virus infection epidemiology and vaccination, Epidemiol. Rev. 28 (2006), pp. 112–125. doi: 10.1093/epirev/mxj009
   Google Scholar
• S. Thornley, C. Bullen, and M. Roberts, Hepatitis B in a high prevalence New Zealand population: A mathematical model applied to infection control policy, J. Theor. Biol. 254 (2008), pp. 599–603. doi: 10.1016/j.jtbi.2008.06.022
   Google Scholar
• J. Wang, J. Pang, and X. Liu, Modelling diseases with relapse and nonlinear incidence of infection: A multi-group epidemic model, J. Biol. Dyn. 8 (2014), pp. 99–116. doi: 10.1080/17513758.2014.912682
   Google Scholar
• J. Wang, R. Zhang, and T. Kuniya, The stability analysis of an SVEIR model with continuous age-structure in the exposed and infectious classes, J. Biol. Dyn. 9 (2015), pp. 73–101. doi: 10.1080/17513758.2015.1006696
   Google Scholar
• R. Williams, Global challenges in liver disease, Hepatology 44 (2006), pp. 521–526. doi: 10.1002/hep.21347
   Google Scholar
• G. Zaman, Y.H. Kang, and I.H. Jung, Stability and optimal vaccination of an SIR epidemic model, BioSystems 93 (2008), pp. 240–249. doi: 10.1016/j.biosystems.2008.05.004
   Google Scholar
• G. Zaman, Y.H. Kang, and I.H. Jung, Optimal treatment of an SIR epidemic model with time delay, BioSystems 98 (2009), pp. 43–50. doi: 10.1016/j.biosystems.2009.05.006
   Google Scholar
• S. Zhang and Y. Zhou, The analysis and application of an HBV model, Appl. Math. Model. 36 (2012), pp. 1302–1312. doi: 10.1016/j.apm.2011.07.087
   Google Scholar
• S.J. Zhao, Z.Y. Xu, and Y. Lu, A mathematical model of hepatitis B virus transmission and its application for vaccination strategy in China, Int. J. Epidemiol. 29 (2000), pp. 744–752. doi: 10.1093/ije/29.4.744
   Google Scholar