Fractional-Order Modeling of the Co-Dynamics of COVID-19 and Hepatitis B: A Vaccination-Based Approach

The co-existence of the COVID-19 pandemic and chronic Hepatitis B infection presents complex challenges for public health systems, necessitating integrated modeling approaches that capture the intricate interactions between co-infections and vaccination dynamics. This study proposes a novel fractional-order mathematical model to describe the co-dynamics of COVID-19 and Hepatitis B using Caputo derivatives, incorporating memory effects that are inherent in biological systems. The model divides the population into epidemiological compartments?such as susceptible, vaccinated, infected (COVID-19 and HBV), co-infected, and recovered?and incorporates vaccination strategies that reduce susceptibility and modify disease progression. A numerical solution is achieved via the Adams?Bashforth?Moulton predictor?corrector method, enabling simulation of disease spread under varying fractional orders. Sensitivity analysis reveals how minor variations in the fractional order significantly impact disease transmission and recovery trends. The results underscore the efficacy of fractional-order modeling in depicting realistic disease dynamics, highlighting the importance of memory in co-infection spread and vaccine effectiveness. This framework offers valuable insights for optimizing immunization strategies and informing public health interventions against both COVID-19 and Hepatitis B.