Analysis of a Fractional-Order Hepatocyte Model of Viral Dynamics Combining Direct-Acting Antiviral Therapy with Alcohol Effects

In this modern world, many people are affected by liver diseases, with the most dangerous strains being hepatitis c virus and hepatitis b virus. This article explores the interaction between hepatocytes and within-host viral dynamics, along with the effectiveness of alcohol and direct-acting antiviral (DAA) medication using fractional derivative formulation. The mathematical model is developed to include memory and genetic factors related to immune responses and persistent viral infections using the Caputo fractional derivative. We establish the existence, uniqueness, positivity, and boundness of the solutions and also prove Hyers–Ulam stability. The next-generation matrix technique is used to determine the reproduction number and the disease-free equilibrium. The qualitative behaviour of the model is examined via the Castillo-Chavez bifurcation theorem, while local stability is analysed using fractional-order stability criteria and also global asymptotic stability is developed by explicitly obtaining the endemic equilibrium. Additionally, we discover that the important factors influencing immune regulation and viral persistence are identified by sensitivity analysis of the reproduction number. Numerical simulations show that the disease decreases by varying the effects of parameters and also show how efficient viral infection management and improved recovery dynamics can possibly be carried out by combining proper treatment procedures with reduced alcohol usage.