Modeling Hepatitis B Virus Transmission Dynamics Using Atangana Fractional Order Network Approach: A Review of Mathematical and Epidemiological Perspectives

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.