A mathematical model of Hepatitis B transmission in Turkey

Year 2019, Volume: 68 Issue: 2, 1586 - 1595, 01.08.2019

Meltem Gölgeli

https://doi.org/10.31801/cfsuasmas.544126

Cited By: 2

Abstract

Hepatitis B infection is one of the serious viral infections that is treating the global health. Turkey has an intermediate endemicity for hepatitis B. In this study, a classical SIR model for hepatitis B virus (HBV) transmission is proposed and analyzed. Based on the available data of Republic of Turkey Ministry of Health, associated parameters are estimated and the fitted model is shown by appropriate simulations. The basic reproductive number is obtained by using the estimated parameters. Finally, we discuss the sensitivity of parameters and the effect of changes of parameters in the spread of disease.

Keywords

Mathematical modeling, SIR models, Hepatitis B

References

• WHO, Global Hepatitis Report, Global Hepatitis Programme, (2017), 1--83.
• Turkish Statistical Institute, Statistics by theme, http://www.tuik.gov.tr/UstMenu.do? metod=temelist
• MacLachlan, J. H. and Cowie, B. C., Hepatitis B Virus Epidemiology, Cold Spring Harbor Perspectives in Medicine, 5(5), (2015), a021410.
• Song, J.E. and Kim, D.Y., Diagnosis of hepatitis B, Ann Transl Med, 4(18) (2016), 338.
• Lewina, S., Ribeiro, R., Walters, T., Lau, G., Bowden, S., Locarnini, S. and Perelson, A.S., Analysis of hepatitis B viral load decline under potent therapy: complex decay profiles observed, Hepatology 34 (2001), 1012--1020.
• Tozun, N., Ozdogan, O., Cakaloglu, Y., Idilman, Y., Karasu, Z., Akarca, U.,Kaymakoglu, S. and Ergonul, O., Seroprevalence of hepatitis B and C virus infections and risk factors in Turkey: a fieldwork TURHEP study, Clinical Microbiology and Infection 21(11), (2015),1020--1026.
• Kwon, S. Y. and Lee, C. H., Epidemiology and prevention of hepatitis B virus infection, The Korean Journal of Hepatology 17(2), (2011), 87--95.
• Toy, M., Önder, F. O., Wörmann, T., Bozdayı, A. M., Schalm, S. W., Borsboom, G. J., van Rosmalen, J., Richardus, J.H. and Yurdaydın, C., Age- and region-specific hepatitis B prevalence in Turkey estimated using generalized linear mixed models: a systematic review, BMC Infectious Diseases 11, (2011), 337.
• Doni Yentur, N., Simsek, Z., Keklik, Z., Gurses, G., Zeyrek, F. Y., Epidemiology of Hepatitis B in the Reproductive-Age Female Farmworkers of Southeastern Turkey, Hepatitis Monthly 14(11), (2017), e22120.
• Ay, P., Torunoglu, M. A., Com, S., cCipil, Z., Mollahaliloğlu, S., Erkoç, Y. and Dilmen, U., Trends of hepatitis B notification rates in Turkey, 1990 to 2012, Euro Surveill. 18(47), (2013), e20636.
• Tosun, S., Viral Hepatitlerin Ülkemizdeki Değişen Epidemiyolojisi, ANKEM Derg. 27(Ek 2) (2013), 128--134.
• MacLachlan, J. H. and Cowie, B. C., Hepatitis B Virus Epidemiology. Cold Spring Harbor Perspectives in Medicine 5(5), (2015), a021410.
• Murray, J.D., Mathematical Biology, Springer-Verlag, New York 1993.
• Jones, D.S. and Sleeman, B.D., Differential Equations and Mathematical Biology, Chapman and Hall/CRC, London 2003.
• Wolberg, J., Data Analysis Using the Method of Least Squares: Extracting the Most Information from Experiments, Springer, Berlin 2006.
• Hale, J. and Kocak, H., Dynamics and Bifurcations, Springer-Verlag, New York 1991.
• Ledder, G., Mathematics for the Life Sciences: Calculus, Modeling, Probability, and Dynamical Systems, Springer, USA 2013.
• Kermack, W.O. and McKendrick, A.G., Contribution to mathematical theory of epidemics, Soc. Lond. A Mat. 115, (1927), 700--721.
• Momoh, A.A., Ibrahim, M.O., Madu, B.A.and Asogwa, K.K., Stability Analysis of Mathematical Model of Hepatitis B Current Research Journal of Biological Sciences 4(5) (2012) 534--537.
• Liang, P., Zu, J. and Zhuang, G., A Literature Review of Mathematical Models of Hepatitis B Virus Transmission Applied to Immunization Strategies From 1994 to 2015, Journal of Epidemiology 28(5), (2018), 221--229.
• Augeraud-Véron, E. and Sari, N., Seasonal dynamics in an SIR epidemic system, Math. Biol. 68 (2014), 701.
• Earn, D.J.D., Rohani, P., Bolker, B.M. and Grenfell, B.T., A simple model for complex dynamical transitions in epidemics, Science 87 (2000), 667--670.
• Hethcote, H.W., The Mathematics of Infectious Diseases, SIAM REVIEW 42(4), (2000), 599--653.
• Ciupe, S.M., Ribiero, R.M., Nelson, P.W. and Perelson, A.S., Modeling the mechanisms of acute hepatitis B virus infection, J Theor Biol. 247 (2007), 23--35.
• Ciupe, S.M., Catlla, A.J., Forde, J., Schaeffer, D.G., Dynamics of hepatitis B virus infection: What causes viral clearance?, Mathematical Population Studies 18 (2011), 87--105.
• Zou, L., Zhang, W. and Ruan, S. Modeling the transmission dynamics and control of hepatitis B virus in China, Journal of Theoretical Biology 262, (2010) 330--338.
• Zhao, S., Su, Z. and Lu Y., A mathematical model of hepatitis B virus transmission and its application for vaccination strategy in China, Int J Epidemiol. 29(4) (2000), 744--752.
• Khan,T., Zaman, G. and Alshomrani, A.S., Spreading dynamic of acute and carrier hepatitis B with nonlinear incidence, PLOS ONE 13(4) (2018), e0191914.
• Lagarias, J.C., Reeds,J.A., Wright, M.H. and Wright, P. E., Convergence Properties of the Nelderâ€"Mead Simplex Method in Low Dimensions, SIAM J. Optim. 9(1), (1998), 112--147.