Authors : Adama Gaye; Otugene Victor Bamigwojo; Idoko Peter Idoko; Adekunle Fatai Adeoye

Volume/Issue : Volume 10 - 2025, Issue 4 - April

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DOI : https://doi.org/10.38124/ijisrt/25apr294

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Abstract : Hepatitis B Virus remains a significant global health challenge, causing chronic liver diseases and posing a high risk of liver cancer and cirrhosis. Despite the availability of vaccines, transmission continues due to complex interactions involving vertical transmission from mother to child, horizontal spread through bodily fluids, and asymptomatic carriers. Traditional mathematical models based on classical differential equations often fail to fully capture the memory effects and non-linear dynamics inherent in Hepatitis B Virus transmission. This shortfall has led to increased interest in fractional calculus-based models that incorporate memory-dependent processes to better represent the disease’s transmission dynamics. This review explores the Atangana fractional order network model as an innovative approach for analyzing the transmission dynamics of Hepatitis B Virus. The model integrates the Atangana-Baleanu-Caputo operator to account for the memory effects present in biological systems, providing a more detailed and realistic understanding of the disease spread. The framework accommodates both vertical and horizontal transmission pathways and incorporates vaccination strategies, making it adaptable to real-world scenarios. Key aspects of the model include parameterization based on experimental data, stability and bifurcation analysis, and numerical simulations that visualize disease behavior under varying conditions. Stability analysis reveals the conditions under which the infection may persist or be eradicated, while bifurcation analysis identifies critical thresholds influencing the system’s behavior. Numerical simulations demonstrate the significant impact of vaccination strategies and population behavior on controlling the infection. The model effectively captures how early-stage interventions and targeted vaccination can substantially reduce infection rates and disease burden. The Atangana fractional order network model offers a powerful tool for understanding and predicting Hepatitis B Virus transmission dynamics. By integrating memory effects and network interactions, the model provides critical insights into disease control and prevention strategies. Its application enhances the design of public health interventions, emphasizing the importance of early vaccinations and tailored strategies to reduce transmission. Future research should focus on refining model assumptions, improving data integration, and expanding applications to other infectious diseases to strengthen global health responses.

Keywords : Hepatitis B Virus Transmission Dynamics Atangana Fractional Order Network Mathematical Epidemiological.

References :

1. Almalahi, M., Aldwoah, K., & Shah, K. (2023). Theoretical and numerical simulations on the Hepatitis B Virus model through a piecewise fractional order. Preprints, 2023101804. https://doi.org/10.20944/preprints202310.1804.v1
2. Bamigwojo, O. V., Ezike, M. C. G., Owhenagbo, P., & Idoko, P. I. (OP), Adedoyin, D. J., Enyejo, L. A., & Chikadum, A. P. (2024). Mathematical Analysis of Hepatitis B Virus Transmission Dynamics in the Absence of Therapy with Atangana-Baleanu Fractional-Order SPQWXY Model. Journal of Advances in Mathematics and Computer Science. Volume 39, Issue 11, Page 1-28, 2024; Article no. JAMCS.124589 ISSN: 2456-9968.
3. Demirci, E. (2022).  A fractional order model of hepatitis B transmission under the effect of vaccination. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 71(2), 390–406. https://doi.org/10.31801 /cfsuasmas.1103630
4. Gao, F., Li, X.-L., Li, W.-Q., & Zhou, X. (2020). Stability analysis of a fractional-order novel hepatitis B virus model with immune delay based on Caputo-Fabrizio derivative. Chaos, Solitons & Fractals, 140, 110436. https://doi.org/10.1016/j.chaos.2020.110436
5. Idoko, I. P., Ijiga, O. M., Enyejo, L. A., Akoh, O., & Isenyo, G. (2024). Integrating superhumans and synthetic humans into the Internet of Things (IoT) and ubiquitous computing: Emerging AI applications and their relevance in the US context. *Global Journal of Engineering and Technology Advances*, 19(01), 006-036.
6. Ijiga, A. C., Aboi, E. J., Idoko, P. I., Enyejo, L. A., & Odeyemi, M. O. (2024). Collaborative innovations in Artificial Intelligence (AI): Partnering with leading U.S. tech firms to combat human trafficking. Global Journal of Engineering and Technology Advances, 2024,18(03), 106-123. https://gjeta.com/sites/de fault/files/GJETA-2024-0046.pdf
7. Khan, T., Qian, Z., Ullah, R., Alwan, B. A., Zaman, G., Al-Mdallal, Q., Khatib, Y., & Kheder, K. (2021). The transmission dynamics of hepatitis B virus via the fractional-order epidemiological model. Computational and Mathematical Methods in Medicine, 2021, 8752161. https://doi.org/10.1155/ 2021/8752161
8. Prakash, M., Rakkiyappan, R., Manivannan, A., Zhu, H., & Cao, J. (2021).  Stability and bifurcation analysis of hepatitis B-type virus infection model. Mathematical Methods in the Applied Sciences, 44(16), 12637–12660. https://doi.org/10.1002/m ma.7198
9. Shah, S. I. A., Khan, M., Farooq, M., Ullah, S., & Alzahrani, E. (2020).  A fractional order model for Hepatitis B virus with treatment via Atangana-Baleanu derivative. Physica A: Statistical Mechanics and its Applications, 543, 122636. https://doi.or g/10.1016 /j.physa.2019.122636
10. Sutradhar, R., & Dalal, D. (2023).  Fractional-order models of hepatitis B virus infection with recycling effects of capsids. Mathematical Methods in the Applied Sciences, 46(5), 5851–5875. https://doi.org/ 10.1002/mma.9415
11. Tilahun, G., Woldegerima, W. A., & Mohammed, N. (2021).  A fractional order model for the transmission dynamics of hepatitis B virus with two-age structure in the presence of vaccination. Biostatistics and Biometrics Open Access Journal, 8(1), 1–10. https://doi.org/10.1080/25765299.2021.1896423
12. Yavuz, M., Özköse, F., Susam, M., & Kalidass, M. (2023). A new modeling of fractional-order and sensitivity analysis for Hepatitis-B disease with real data. Fractal and Fractional, 7(2), 165. https://doi.org/10.3390/fractalfract7020165
13. Zarin, R. (2022).  Modeling and numerical analysis of fractional order hepatitis B virus model with harmonic mean type incidence rate. Computer Methods and Programs in Biomedicine, 225, 107040. https://doi.org/10.1080/10255842.20 22.2103371