A COMPUTATIONAL AND FRACTIONAL MATHEMATICAL MODEL FOR ASSESSING HEPATITIS B WITH OPTIMAL THERAPY

Abstract

This paper presents a mathematical study applied to Hepatitis B disease utilizing fractional calculus and numerical methods. We begin by discussing mathematical fundamentals, focusing on fractional calculus concepts and relevant numerical aspects for disease modeling. We then formulate the problem, describing a nonlinear fractional differential system that models hepatitis B virus (HBV) infection and its response to drug therapy. A detailed theoretical analysis explores system properties and biological implications. We provide a qualitative analysis of the model, discussing important dynamic behaviors such as stability and parameter sensitivity. Subsequently, numerical analysis is performed to validate the model and estimate unknown parameters from patient data. Our findings include significant insights into biological parameters and their impact on therapeutic response. We conclude that the proposed fractional-order model is effective, offering optimal therapeutic strategies for hepatitis B.