Mathematical Modeling the Effects of Vaccination on HBV Infection in Thailand
Abstract
Hepatitis B virus (HBV) infection is a disease characterized by inflammation of the liver. There are two types of hepatitis B virus infection, acute hepatitis B and chronic hepatitis B. The chronic hepatitis B is the most significant factor leading to liver cancer and cirrhosis. There are approximately 350 million people infected with the HBV worldwide, and 75% of them are from Asia. In Thailand, there are approximately 3% of the populations who are infected by HBV. Nowadays, the number of people who are infected by HBV is decreased due to the present of vaccination. However, the number of infected people is still at high level and could be further reduced. Therefore, in this research we study and explore further by constructing and analyzing mathematical models relating to vaccination in the form of SVIR models. Numerical analysis is performed to explore the effect of some particular parameters to the overall dynamics. The basic reproduction number is also calculated. This is to find some approaches to control the epidemic or reduce number of patients with HBV in Thailand. Keywords : hepatitis B, vaccine, mathematical model, numerical analysisReferences
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Universal hepatitis B vaccination in Taiwan and the incidence of hepatocellular carcinoma in children. Taiwan Childhood Hepatoma Study Group. N Engl J., 336,1855-1859.
Chang, M.H., You, S.L., Chen, C.J., Liu, C.J., Lai, M.W., Wu, T.C., et al. (2016). Long-term Effects of
Hepatitis B Immunization of Infants in Preventing Liver Cancer. Gastroenterology, 151,472–480.
Chongsrisawat, V., Yoocharoen, P., Theamboonlers, A., Tharmaphornpilas, P., Warinsathien, P.,
Sinlaparatsamee, S., Paupunwatana, S., Chaiear, K., Khwanjaipanich, S. and Poovorawan, Y. (2006). Hepatitis B seroprevalence in Thailand: 12 years after hepatitis B vaccine integration into the national expanded programme on immunization. Tropical Medicine & International Health, 11(10),
1496-1502.
Diekmann, O., Heesterbeek, J. and Metz, J.A. (1990). On the definition and the computation of the
basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations.
J. Math. Biol., 28(4), 365-382.
Dontwi, K., Obeng-Denteh, W., Obiri-Apraku, L. and Andam, E. A. (2014). Modelling hepatitis B in
a high prevalence district in Ghana. British Journal of Mathematics & Computer Science, 4(7),
969-988.
Edmunds, W.J., Medley, G.F. and Nokes, D.J. (1996). Vaccination against hepatitis B virus in highly
endemic area: waning vaccine-induced immunity and the need for booster doses. Trans. R. Soc.
Trop. Med. Hyg., 90, 436–440.
Elise, M.B., Ian, T.W., Craig, N.S. and Mary, E. (2000). Risk and Management of Blood-
Borne Infections in Health Care Workers. Chamberiand. Clin Microbiol Rev,13(3), 385–407.
Henry, J.P., Simona, C.K., Su, H.W., Laura, C.W. and Chau, T.S. (2014). Chronic hepatitis B and liver
cancer risks among Asian immigrants in New York City: results from a large, community-based screening, evaluation, and treatment program. Cancer Epidemiol Biomarkers Prev., 23(11),
2229-2239.
Kimbir, A.R., Aboiyar, T., Abu, O. and Onah, E.S. (2014). Modelling Hepatitis B Virus Transmission Dynamics
In The Presence of Vaccination and Treatment. Mathematical Theory and Modeling Vol.4, No.12,
2224-5804.
Lim, K. S., Taam wong, V., Fulford, K.W.M., Catterall, R.D., Briggs, M., and Dane, D.S. (1977). Role of sexual and non-sexual practices in the transmission of hepatitis B. British Journal of Venereal Diseases, 53, 190-192.
Nowak, M., Bonhoeffer, S., Hill, A., Boehme, R., Thomas, H., and McDade, H. (1996). Viral dynamics
in hepatitis B virus infection, Proc. Natl Acad. Sci. USA 93, 4398-4402.
Richard, G. and Hock Foong, L. (2011). Treatment of Hepatitis B in Decompensated Liver
Cirrhosis. International Journal of Hepatology Volume 2011, 11 pages.
Van den Driessche, P. and Watmough, J. (2002). Reproduction numbers and sub-threshold endemic
equilibria for compartmental models of disease transmission. Math. Biosci. ,180, 29-48
Williams, J.R., Nokes, D.J., Medley, G.F. and Anderson, R.M. (1996). The transmission dynamics of hepatitis B in the UK: A mathematical model for evaluating costs and effectiveness of immunization programmes. Epidemiol Infect., 116(1),71-89.
Zou, L. and Zhang, W. (2009). Modeling the transmission dynamics and control of hepatitis B virus in China. Journal of Theoretical Biology, 10, 1-9.
Bumrungrad International. Better Health (2008). Retrieved January 2, 2017, from
https://www.bumrungrad.com/th/betterhealth/2551/high-performance/threat-grows-for-millions-in-thailand-and-asia.
Bureau of Epidemiology, Department of Disease Control, MoPH, Thailand (2015). Retrieved January 2, 2017,
from http://www.boe.moph.go.th/boedb/surdata/disease.php?ds=12.
Foundation for Liver Research. Hepatitis B: Out of the shadows (A report into the impact of hepatitis B on the
nation’s health). (2004). Retrieved January 18, 2017, from http://www.liver-research.org.uk/liver-research-files/Hepatitis-B---Out-of-the-Shadows.pdf
National Institute of Diabetes and Digestive and Kidney Diseases (NIDDK), (2012). Retrieved October 25, 2016, from, https://www.niddk.nih.gov/health-information/liver-disease/viral-hepatitis/hepatitis-b
WHO (World Health Organiaztion), Hepatitis B Fact Sheet No. 204. The World Health Organisation, Geneva,
Switerland, 2013. Retrieved January 2, 2017, from,
http://www.who.int/mediacentre/factsheets/fs204/en/.
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Published
2017-08-08
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บทความวิจัยจากการประชุมวิชาการระดับชาติ"วิทยาศาสตร์วิจัย"ครั้งที่ 9
