Modeling the dynamics of the Hepatitis B virus via a variable-order discrete system

TL;DR

This paper models hepatitis B virus dynamics using a novel variable-order discrete system, providing insights into stability and solution properties through mathematical analysis and numerical simulations.

Contribution

It introduces a variable-order discrete model for hepatitis B virus dynamics and analyzes its stability, existence, and positivity properties using fixed-point and stability techniques.

Findings

Model exhibits bounded and positive solutions

Stability analyzed via basic reproduction number

Numerical simulations demonstrate model behavior

Abstract

We investigate the dynamics of the hepatitis B virus by integrating variable-order calculus and discrete analysis. Specifically, we utilize the Caputo variable-order difference operator in this study. To establish the existence and uniqueness results of the model, we employ a fixed-point technique. Furthermore, we prove that the model exhibits bounded and positive solutions. Additionally, we explore the local stability of the proposed model by determining the basic reproduction number. Finally, we present several numerical simulations to illustrate the richness of our results.