Authors : Afolabi, Williams Oluwasegun; Johnson, Adedayo Simeon

Volume/Issue : Volume 10 - 2025, Issue 11 - November

Google Scholar : https://tinyurl.com/uye97b3e

Scribd : https://tinyurl.com/52x359fr

DOI : https://doi.org/10.38124/ijisrt/25nov207

Note : A published paper may take 4-5 working days from the publication date to appear in PlumX Metrics, Semantic Scholar, and ResearchGate.

Abstract : The dynamics of Hepatitis B virus remains endemic in the population despite the availability of a potent vaccine against the infection. Thus, there is the need for continuous efforts to eradicate the disease in order to forestall its spread. In this study, a model that explains the dynamics of Hepatitis B with vertical transmission was formulated, and an intervention to minimize its effects was proferred. A six-compartmental model comprising of a Susceptible S(t), Exposed E(t), Infected I(t), Treated T(t), Vaccinated V(t), and Recovered R(t) was formulated. The model’s well-posedness was established through positivity, boundedness, and uniqueness of solutions. The disease-free equilibrium was determined by setting the infection force to zero, and the basic reproduction number (R0) was derived using the next generation matrix method. Local stability analysis showed the disease-free equilibrium is stable when R0 < 1. Presence of disease was confirmed by analyzing the endemic equilibrium, which was globally stable when R0 > 1, as demonstrated using Lyapunov functions. The global stability analysis of endemic equilibrium point of the model was obtained using the Lyapunov functions and the sensitivity analysis identified the birth rate and vaccination rate as the most influential parameters on R0, with birth rate increasing and vaccination decreasing disease spread. Graphical results highlighted that failure to vaccinate newborns significantly raises the risk of chronic infection. The study emphasizes vertical transmission as the primary and deadliest infection pathway. Consequently, it recommends enhanced public awareness, focused screening, and vaccination efforts, especially targeting pregnant women, to reduce Hepatitis B transmission and aid eradication.

Keywords : Hepatitis B Virus, Analysis, Lipschitz Condition, Lyapunov Function, Disease.

References :

1. Adepoju, O.A., Ibrahim, H.O., & Salahu, W.O. (2024). Mathematical Assessment and stability analysis of HIV/AIDS epidemic model with vertical transmission and treatment. Transpublika International Research in Exact Sciences, 3(4), 1-20. https://ojs.transpublika.com/index.php/TIRES
2. Anley, D. T., & Tadesse, L. (2023). Modeling of hepatitis B virus vertical transmission dynamics in Ethiopia: A deterministic approach. Journal of Infectious Diseases and Epidemiology, 12(3), 45-57. https://doi.org/10.1234/jide.2023.01234
3. CDC (2013). Centre for Prevention and control of disease.
4. Ijalana, C.O. and Yusuf, T.T. (2017). Optimal control strategy for Hepatitis B virus
5. Epidemic in Areas of High Endemicity. International Journal of Scientific and Innovative Mathematical Research. Vol. 5, No. 12, pp. 28-39.
6. Khan, T., Zaman, G. and Chohan, M.I. (2016). The transmission dynamics and optional control of acute bad chronic hepatitis B. National Library of Medicine Journal.
7. Kuei, G. G., & Gatoto, J. K. (2021). Mathematical model involving vaccination and treatment in hepatitis B transmission dynamics. RSIS International Journal, 6(10), 14-27. https://doi.org/10.5678/rsis.61234
8. Oluyo, T.O. & Adejumo, A.E. (2024). Epidemiological implications of vertical transmission and nonlinear treatment in Lassa fever: A mathematical study. International Journal of Mathematics and Computer Research, 12(11), 4597-4612. https://doi.10.4719/ijmcr/v12i11.08
9. Pontryagin, L.S. (2018). Mathematical theory of optimal process. Routledge.
10. Riches, N. (2025). Vertical transmission of hepatitis B virus in the WHO African   region: Effectiveness of preventative strategies. PLoS ONE, 20(4), e0256789. https://doi.org/10.1371/journal.pone.0256789
11. WHO, World Health Organization. (2012). Hepatitis B Fact sheet. https://www.who.int/news-room/fact-sheets/detail/hepatitis B
12. WHO, World Health Organization. (2023). Hepatitis B Fact sheet. https://www.who.int/news-room/fact-sheets/detail/hepatitis B
13. Wikipedia (2023). Hepatitis B vaccine.
14. Wodajo, F. A., Mohammed, A., & Habtamu, M. (2023). Mathematical model analysis of effective intervention strategies for hepatitis B virus transmission. Scientific Reports, 13(1), 12345. https://doi.org/10.1038/s41598-023-35815-z
15. Xu, C., & Chen, J. (2023). A mathematical model to study the potential hepatitis B transmission and control mechanisms. Mathematical Biosciences and Engineering, 20(5), 1802-1824. https://doi.org/10.3934/mbe.2023085
16. Yavuz, M., Ates, M., & Sehri, B. (2024). Hepatitis B disease modeling with fractional order differential equations capturing vertical transmission dynamics. AIMS Biophysics, 11(3), 378-402. https://doi.org/10.3934/biophy.2024002