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Hepatit-B İçin Yeni Bir Matematiksel Model ve Modelde Dikey Bulaşın Etkisi

Year 2025, Volume: 7 Issue: 2, 214 - 227, 31.08.2025

Mehmet Yavuz , Naime Büşra Bayraktar , Kübra Akyüz , Feyza Nur Özdemir

Abstract

Bu makalede, Hepatit virüsünün bulaşma dinamiklerini araştırmak için Hepatit B'nin yeni bir matematiksel modeli oluşturulmuştur. Model, dikey bulaşmayı dikkate alarak geliştirilmiştir. Modelde, duyarlı, latent, akut, taşıyıcı, iyileşen ve aşılanmış popülasyonlar dikkate alınmıştır. Ayrıca, pozitiflik ve hastalıksız denge noktası belirlenmiştir. Son olarak, sayısal sonuçlar elde edilmiş ve hastalığın gelecekteki seyrini tahmin etmek için biyolojik yorumları yapılmıştır.

Keywords

Hepatit-B virüsü Matematiksel modelleme Göç faktörü Dikey geçiş

Supporting Institution

This research was supported by Scientific and Technological Research Council of Türkiye (TÜBİTAK) under the undergraduate research project.

References

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A New Mathematical Model for Hepatitis-B and the Effect of Vertical Transmission in the Model

Year 2025, Volume: 7 Issue: 2, 214 - 227, 31.08.2025

Mehmet Yavuz , Naime Büşra Bayraktar , Kübra Akyüz , Feyza Nur Özdemir

Abstract

In this paper, a new mathematical model of Hepatitis B is constructed to investigate the dynamics of the transmission of the Hepatitis virus. The model is developed by considering the vertical transmission. In the model, susceptible, latent, acute, carrier, recovered, and vaccinated populations are taken into account. Moreover, positivity is performed, and disease-free equilibrium point is calculated. Finally, the numerical results and their biological interpretations are performed to estimate the future directions of the disease.

Keywords

Hepatitis-B virus Mathematical modeling Migration factor Vertical transmission

Supporting Institution

This research was supported by Scientific and Technological Research Council of Türkiye (TÜBİTAK) under the undergraduate research project.

References

  • [S.M. Ciupe, R.M. Ribeiro, P.W. Nelson, G. Dusheiko, A.S. Perelson, The role of cells refractory to productive infection in acute hepatitis B viral dynamics, Proceedings of the National Academy of Sciences. 104(12) (2007), 5050-5055. doi: 10.1073/pnas.0603626104
  • F.F. Chenar, Y.N. Kyrychko, K.B. Blyuss, Mathematical model of immune response to hepatitis B, Journal of Theoretical Biology. 447 (2018), 98-110. doi: 10.1016/j.jtbi.2018.03.025
  • Acıbadem Yayın Kurulu, (2021). https://www.acibadem.com.tr/ilgi-alani/hepatit-b/ (erişim 10 Mayıs 2024).
  • A. Çilli, K. Ergen, Salgın hastalıkların tahmininde kullanılan SI ve SIS modellerin uygulamaları, Bitlis Eren Üniversitesi Fen Bilimleri Dergisi. 8(3) (2019), 755-761. doi: 10.17798/bitlisfen.522533
  • A. Costa, M. Pires, R. Resque, S.S.M.S. Almeida, Mathematical modeling of the infectious diseases: key concepts and applications, Journal of Infectious Diseases and Epidemiology. 7(5) (2021), 209. doi: 10.23937/2474-3658/1510209
  • U.S. Bashir, A. Umar, Mathematical analysis of hepatitis B virus model with interventions in Taraba state, Nigeria. International Journal of Development Mathematics (IJDM). 1 (1) (2024). doi: 10.62054/ijdm/0101.14
  • A. Kiemtore, W.O. Sawadogo, I. Zangré, P.O.F. Ouedraogo, I. Mouaouia, Estimation of parameters for the mathematical model of the spread of hepatitis B in Burkina Faso using grey wolf optimizer, International Journal of Analysis and Applications. 22 (2024), 48-48. doi: 10.28924/2291-8639-22-2024-48
  • D.M. Li, B. Chai, A dynamic model of hepatitis B virus with drug-resistant treatment, AIMS Mathematics. 5(5) (2020), 4734-4753. doi: 10.3934/math.2020303
  • P. Liu, A. Din, R. Zarin, Numerical dynamics and fractional modeling of Hepatitis B virus model with non-singular and non-local kernels, Results in Physics. 39 (2022), 105757. doi: 10.1016/j.rinp.2022.105757 [ A.M. Elaiw, M.A. Alghamdi, S. Aly, Hepatitis B virus dynamics: modeling, analysis, and optimal treatment scheduling, Discrete Dynamics in Nature and Society. 1 (2013). doi: 10.1155/2013/712829
  • T. Khan, S. Ahmad, G. Zaman, Modeling and qualitative analysis of a hepatitis B epidemic model, Chaos: An Interdisciplinary Journal of Nonlinear Science. 29(10) (2019). doi: 10.1063/1.5111699
  • M.J. de Villiers, I. Gamkrelidze, T.B. Hallett, S. Nayagam, H. Razavi, D. Razavi-Shearer, Modelling hepatitis B virus infection and impact of timely birth dose vaccine: a comparison of two simulation models, PLoS One. 15 (8) (2020). e0237525 doi: 10.1371/journal.pone.0237525
  • D. Otoo, I.O. Abeasi, S. Osman, E.K. Donkoh, Mathematical modeling and analysis of the dynamics of hepatitis b with optimal control, Communications in Mathematical Biology and Neuroscience. (2021). doi: 10.28919/cmbn/5733
  • L.C. Cardoso, R.F. Camargo, F.L.P. dos Santos, J.P.C. Dos Santos, (2021). Global stability analysis of a fractional differential system in hepatitis B. Chaos, Solitons & Fractals. 143 (2021). 110619. doi: 10.1016/j.chaos.2020.110619
  • M. Farman, A. Ahmad, H. Muslim, M.O. Ahmad, (2019). Dynamical behavior of hepatitis B fractional-order model with modeling and simulation, Journal of Biochemical Technology. 10(3) (2019), 11-17.
  • V. Reinharz, Y. Ishida, M. Tsuge, K. Durso-Cain, T.L. Chung, C. Tateno, et al. Understanding hepatitis B virus dynamics and the antiviral effect of interferon alpha treatment in humanized chimeric mice, Journal of Virology. 95(14) (2021), 10-1128. doi: 10.1128/jvi.00492-20
  • A.M. Ortega-Prieto, C. Cherry, H. Gunn, M. Dorner, In vivo model systems for hepatitis B virus research, ACS Infectious Diseases. 5(5) (2018), 688-702. doi: 10.1021/acsinfecdis.8b00223
  • T. Khan, F.A. Rihan, M. Ibrahim, S. Li, A.M. Alamri, S.A. AlQahtani, Modeling different infectious phases of hepatitis B with generalized saturated incidence: An analysis and control, Mathematical Biosciences and Engineering. 21(4) (2024), 5207-5226. doi: 10.3934/mbe.2024230
  • A. Friedman, N. Siewe, Chronic hepatitis B virus and liver fibrosis: A mathematical model, PLoS One. 13(4) (2018), e0195037. doi: 10.1371/journal.pone.0195037
  • O. Oludoun, O. Adebimpe, J. Ndako, M. Adeniyi, O. Abiodun, B. Gbadamosi, The impact of testing and treatment on the dynamics of Hepatitis B virus, F1000Research. 10 (2021). doi: 10.12688/f1000research.72865.1
  • R. Ikram, A. Khan, M. Zahri, A. Saeed, M. Yavuz, P. Kumam, Extinction and stationary distribution of a stochastic COVID-19 epidemic model with time-delay, Computers in Biology and Medicine. 141 (2022), 105115. doi: 10.1016/j.compbiomed.2021.105115
  • I.U. Haq, N. Ali, and K. S. Nisar, An optimal control strategy and Grünwald-Letnikov finite-difference numerical scheme for the fractional-order COVID-19 model, Mathematical Modelling and Numerical Simulation with Applications. 2(2) (2022), 108-116. doi: 10.53391/mmnsa.2022.009
  • H. Joshi, B.K. Jha, and M. Yavuz, Modelling and analysis of fractional-order vacci-nation model for control of COVID-19 outbreak using real data, Mathematical Biosciences and Engineering. 20(1) (2022), 213-240. doi: 10.3934/mbe.2023010
  • H. Joshi, M. Yavuz, S. Townley, and B. K. Jha, Stability analysis of a non-singular fractional-order covid-19 model with nonlinear incidence and treatment rate, Physica Scripta. 98(4) (2023), 045216. doi: 10.1088/1402-4896/acbe7a
  • M. Yavuz, F.Ö. Coşar, F. Günay, F.N. Özdemir, A new mathematical modeling of the COVID-19 pandemic including the vaccination campaign, Open Journal of Modelling and Simulation. 9(3) (2021), 299-321. doi: 10.4236/ojmsi.2021.93020
  • A.S. Waziri, E.S. Massawe, O.D. Makinde, Mathematical modelling of HIV/AIDS dynamics with treatment and vertical transmission, Journal Applied Mathematics. 2(3) (2012), 77-89. doi: 10.5923/j.am.20120203.06
  • D. Wodarz, M.A. Nowak, Mathematical models of HIV pathogenesis and treatment, BioEssays. 24(12) (2002), 1178-1187. doi: 10.1002/bies.10196
  • T.K. Ayele, E.F.D. Goufo, S. Mugisha, Mathematical modeling of HIV/AIDS with optimal control: a case study in Ethiopia, Results in Physics. 26 (2021), 104263. doi: 10.1016/j.rinp.2021.104263
  • S. Wang, Y. Pan, Q. Wang, H. Miao, A.N. Brown, L. Rong, Modeling the viral dynamics of SARS-CoV-2 infection, Mathematical Biosciences. 328 (2020), 108438. doi: 10.1016/j.mbs.2020.108438
  • S.M. Ciupe, N. Tuncer, Identifiability of parameters in mathematical models of SARS-CoV-2 infections in humans, Scientific Reports. 12(1) (2022), 14637. doi: 10.1038/s41598-022-18683-x
  • G. Gonzalez-Parra, D. Martínez-Rodríguez, R.J. Villanueva-Micó, Impact of a new SARS-CoV-2 variant on the population: A mathematical modeling approach, Mathematical and Computational Applications, 26(2) (2021). 25. doi: 10.3390/mca26020025
  • A. Atifa, M.A. Khan, K. Iskakova, F.S. Al-Duais, I. Ahmad, Mathematical modeling and analysis of the SARS-Cov-2 disease with reinfection, Computational Biology and Chemistry. 98 (2022), 107678. doi: 10.1016/j.compbiolchem.2022.107678
  • M. Yavuz, F. Özköse, M. Akman, Z.T. Tastan, A new mathematical model for tuberculosis epidemic under the consciousness effect, Mathematical Modelling and Control. 3(2) (2023), 88-103. doi: 10.3934/mmc.2023009
  • E.D. Ginting, D. Aldila, I.H. Febriana, A deterministic compartment model for analyzing tuberculosis dynamics considering vaccination and reinfection, Healthcare Analytics. 5 (2024), 100341. doi: 10.1016/j.health.2024.100341
  • J. Wang, G. Lyu, Analysis of an age-space structured tuberculosis model with treatment and relapse, Studies in Applied Mathematics. 153(1) (2024), e12700. doi: 10.1111/sapm.12700
  • E.M. Delgado Moya, J.A. Ordoñez, F. Alves Rubio, M. Niskier Sanchez, R.B. de Oliveira, R. Volmir Anderle, D. Rasella, A Mathematical Model for the Impact of 3HP and Social Programme Implementation on the Incidence and Mortality of Tuberculosis: Study in Brazil, Bulletin of Mathematical Biology. 86(6) (2024), 1-25. doi: 10.1007/s11538-024-01285-1
  • A.A. Gebremeskel, H.E. Krogstad, Mathematical modelling of endemic malaria transmission, American Journal of Applied Mathematics. 3(2) (2015), 36-46. doi: 10.11648/j.ajam.20150302.12
  • S.I. Oke, M.M. Ojo, M.O. Adeniyi, M.B. Matadi, Mathematical modeling of malaria disease with control strategy, Communications in Mathematical Biology and Neuroscience. (2020), Article-ID: 43. doi: 10.28919/cmbn/4513
  • M. Osman, I. Adu, Simple mathematical model for malaria transmission, Journal of Advances in Mathematics and Computer Science. 25(6) (2017), 1-24. doi: 10.9734/JAMCS/2017/37843
  • S. Olaniyi, O.S. Obabiyi, Mathematical model for malaria transmission dynamics in human and mosquito populations with nonlinear forces of infection, International Journal of Pure and Applied Mathematics. 88(1) (2013), 125-156. doi: http://dx.doi.org/10.12732/ijpam.v88i1.10
  • P. A. Naik, Z. Eskandari, M. Yavuz, & Z. Huang, Bifurcation results and chaos in a two-dimensional predator-prey model incorporating Holling-type response function on the predator, Discrete and Continuous Dynamical Systems-S. (2024). doi: 10.3934/dcdss.2024045
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There are 56 citations in total.

Details

Primary Language English
Subjects Biological Mathematics
Journal Section Articles
Authors

Mehmet Yavuz 0000-0002-3966-6518

Naime Büşra Bayraktar 0000-0001-7584-437X

Kübra Akyüz 0009-0006-6642-1117

Feyza Nur Özdemir 0000-0001-7803-7725

Publication Date August 31, 2025
Submission Date May 23, 2024
Acceptance Date December 18, 2024
Published in Issue Year 2025 Volume: 7 Issue: 2

Cite

APA Yavuz, M., Bayraktar, N. B., Akyüz, K., Özdemir, F. N. (2025). A New Mathematical Model for Hepatitis-B and the Effect of Vertical Transmission in the Model. Necmettin Erbakan Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, 7(2), 214-227.
AMA Yavuz M, Bayraktar NB, Akyüz K, Özdemir FN. A New Mathematical Model for Hepatitis-B and the Effect of Vertical Transmission in the Model. NEJSE. August 2025;7(2):214-227.
Chicago Yavuz, Mehmet, Naime Büşra Bayraktar, Kübra Akyüz, and Feyza Nur Özdemir. “A New Mathematical Model for Hepatitis-B and the Effect of Vertical Transmission in the Model”. Necmettin Erbakan Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 7, no. 2 (August 2025): 214-27.
EndNote Yavuz M, Bayraktar NB, Akyüz K, Özdemir FN (August 1, 2025) A New Mathematical Model for Hepatitis-B and the Effect of Vertical Transmission in the Model. Necmettin Erbakan Üniversitesi Fen ve Mühendislik Bilimleri Dergisi 7 2 214–227.
IEEE M. Yavuz, N. B. Bayraktar, K. Akyüz, and F. N. Özdemir, “A New Mathematical Model for Hepatitis-B and the Effect of Vertical Transmission in the Model”, NEJSE, vol. 7, no. 2, pp. 214–227, 2025.
ISNAD Yavuz, Mehmet et al. “A New Mathematical Model for Hepatitis-B and the Effect of Vertical Transmission in the Model”. Necmettin Erbakan Üniversitesi Fen ve Mühendislik Bilimleri Dergisi 7/2 (August2025), 214-227.
JAMA Yavuz M, Bayraktar NB, Akyüz K, Özdemir FN. A New Mathematical Model for Hepatitis-B and the Effect of Vertical Transmission in the Model. NEJSE. 2025;7:214–227.
MLA Yavuz, Mehmet et al. “A New Mathematical Model for Hepatitis-B and the Effect of Vertical Transmission in the Model”. Necmettin Erbakan Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, vol. 7, no. 2, 2025, pp. 214-27.
Vancouver Yavuz M, Bayraktar NB, Akyüz K, Özdemir FN. A New Mathematical Model for Hepatitis-B and the Effect of Vertical Transmission in the Model. NEJSE. 2025;7(2):214-27.
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