___

• Anderson, R. M., May, R. M., Vaccination and herd immunity, Nature, 318 (1985), 323-329.
• Diekmann, O., Heesterbeek, J. A. P., Metz, J. A. J., On the definition and computation of the basic reproduction ratio $R_{0}$ in models for infectious diseases in heterogeneous populations, J. Math. Biol., 28 (1990), 365-382.
• Ding, Y., Ye, H., A fractional-order differential equation model of HIV infection of $CD4^{+}T-$Cells, Mathematical and Computer Modeling, 50 (2009), 386-392.
• El-Saka, H. A. A., The fractional-order SIS epidemic model with variable population size, Journal of Egyptian Mathematical Society, 22(1) (2014), 50-54.
• European Center for Disease Prevention and Control, Hepatitis B - Annual Epidemiological Report (2016). https://www.ecdc.europa.eu/en/publications-data/hepatitis-b-annual epidemiological-report-2016-2014-data / Accessed 21.09.2020.
• Farman, M., Ahmad, A., Umer, S. A., Hafeez, A., A mathematical analysis and modeling of hepatitis B model with non-integer time fractional derivative, Communications in Mathematics and Applications, 10(3) (2019), 571-584.
• Fattorich, G., Bortolotti, F., Donato, F., Natural history of chronic hepatitis B: special emphasis on disease progression and prognostic factors, J. Hepatol., 48(2) (2008), 335-352. doi: 10.1016/j.jhep.2007.11.011
• Ferrari, M. J., Perkins, S. E., Pomeroy, L. W., Bjornstad, O. N., Pathogens, social networks, and the paradox of transmission scaling, Interdisciplinary Perspectives on Infectious Diseases, Article ID 267049 (2011). doi:10.1155/2011/267049.
• Geard, N., Glass, K., McCaw, J. M., McBryde, E. S., Korb, K. B., Keeling, M. J., McVernon, J., The effects of demographic change on disease transmission and vaccine impact in a household structured population, J. Epidemics, 13 (2015), 56-64.
• Golgeli, M., A Mathematical model of hepatitis B transmission in Turkey, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 68(2) (2019), 1586-1595.
• Khan, T., Zaman, G., Chohan, M. I., The transmission dynamic and optimal control of acute and chronic hepatitis B, Journal of Biological Dynamics, 11(1) (2017), 172-189.
• Liang, P., Zu, J., Zhiang, G., A Literature review of mathematical models of hepatitis B virus transmission applied to immunization strategies from 1994 to 2015, J. Epidemiol., 28(5) (2018), 221-229.
• Lin, W., Global existence theory and chaos control of fractional differential equations, JMAA, 332 (2007), 709–726.
• Marcelin, P., Pequignot, F., Delarocque-Astagneau, E., Zarski, J., Ganne, N., Hillon, P., Antona, D., Bovet, M., Mechain, M., Asselah, T., Desenclos, J., Jougla, E., Mortality related to chronic hepatitis B and chronic hepatitis C in France: Evidence for the role of HIV coinfection and alcohol consumption, Journal of Hepatology, 48 (2008), 200-207.
• Mardh, O., Quinten, C., Amato-Gauci, A. J., Duffell, E., Mortality from liver diseases attributable to hepatitis B and C in the EU/EEA – descriptive analysis and estimation of 2015 baseline, Infectious Diseases, (2020). doi:10.1080/23744235.2020.1766104
• Mc Lean, A. R., Blumberg, B. S., Modeling the impact of mass vaccination against hepatitis B. I. model formulation and parameter estimation, Proc.Biol.Sci., 256 (1994), 7-15.
• Mouaouine, A., Boukhouima, A., Hattaf, K., Yousuf, N., A fractional order SIR epidemic model with nonlinear incidence rate, Advances in Difference Equations, 160 (2018).
• Özalp, N., Demirci, E., A Fractional order SEIR model with vertical transmission, Mathematical and Computer Modelling, 54(1-2) (2011), 1-6.
• Podlubny, I., Fractional Differential Equations, Volume 198: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications, (1st ed.), Academic Press, 1998.
• Republic of Turkey Ministry of Health, Vaccine Portal, asi.saglik.gov.tr/liste/4-hepatit-bhastaligi-nedir.html / Accessed 16.09.2020.
• Kodani, M., Schillie, S. F., Hepatitis B, manual for the surveillance of vaccine-preventable diseases, Edited by: Roush, S. W., Baldy, L. M., Hall, M. A. K., Centers for Disease Control and Prevention, Atlanta GA, March 13 2020.
• Medley, G. F., Lindop, N. A., Edmunds, W. J., Nokes, D. J., Hepatitis-B virus endemicity: heterogeneity, catastrophic dynamics and control, Nature Medicine, 7 (2001), 619-624. https://doi.org/10.1038/87953
• Saeedian, M., Khalighi, M., Azimi-Tafreshi, N., Jafari, G. R., Ausloos, M., Memory effects on epidemic evolutions: The susceptible-infected-recovered epidemic model, Physical Review E, 95(022409) (2017).
• Tosun, S., Hepatit B A¸sılaması ve ¨Ulkemizde Hepatit A¸sılama Sonu¸cları, In Tabak, F., Balık, İ. (Eds.), Viral Hepatit 2013 (pp.413-39), Viral Hepatitle Savaşım Dernegi Yayını, İstanbul Medikal Yayıncılık, İstanbul, 2013.
• Tosun, S., Pregnancy and hepatitis B virus infection, Medditerr. J. Infect. Microb. Animicrob., 5(4) (2016).
• Toy, M., Onder, F. O., W¨ormann, T., Bozdayi, A. M., Schalm, S. W., Borsboom, G. J., van Rosmalen, J., Richardus, J. H., Yurdaydin, C., Age and region specific hepatitis B prevalence in Turkey estimated using generalized linear mixed models: a systematic review, BMC Infectious Diseases, 11(337) (2011). doi: 10.1186/1471-2334-11-337
• Tozun, N., Ozdogan, O., Cakaloglu, Y., Idilman, R., Karasu, Z., Akarca, U., Kaymakoglu, S., Ergonul, O., Seroprevalence of hepatitis B and C virus infections and risk factors in Turkey: a fieldwork TURHEP study, Clin. Microbiol. Infect., 21(11) (2015), 1020-1026. doi:10.1016/j.cmi.2015.06.028
• Turkish Statistical Institution, TUIK. http://www.tuik.gov.tr/PreIstatistikTablo.do?istab id=1636/ Accessed 23.09.2020.
• Ullah, S., Khan, M. A., Farooq, M., A new fractional model for the dynamics of the hepatitis B virus using the Caputo-Fabrizio derivative, The European Physical Journal Plus, 133(237) (2018). doi: 10.1140/epjp/i2018-12072-4
• Van den Driessche, P., Watmough, J., Reproduction numbers and sub-treshold equilibria for compartmental models of disease transmission, Mathematical Biosciences, 180(1-2) (2002), 29-48.
• Van den Driessche, P., Watmough, J., Further Notes on the Basic Reproduction Number, Mathematical Epidemiology (pp.159-178), Springer, Berlin, Heidelberg, 2008.
• Van den Driessche, P., Reproduction numbers of infectious disease models, Infectious Disease Modelling, 2(3) (2017), 288-303.
• World Health Organization, https://www.who.int/news-room/fact-sheets/detail/hepatitisb/Accessed 28 May 2022.
• World Health Organization Western Pacific Region, hepatitis B control through immunization: a reference guide, WHO, ISBN: 9789290616696, 2014. https://www.who.int/newsroom/fact-sheets/detail/hepatitis-b/ Accessed 28 May 2022.
• Zou, L., Zhang, W., Ruan, S., Modeling the transmission dynamics and control of hepatitis B virus in China, Journal of Theoretical Biology, 262(2) (2010), 330-338.