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Development of a Hepatitis B Virus Reporter System to Monitor the Early Stages of the Replication Cycle

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Approximate solutions for HBV infection with stability analysis using LHAM during antiviral therapy.

M Aniji¹, N Kavitha¹, S Balamuralitharan²

¹Department of Mathematics, University College of Engineering, Rajamadam, Pattukkottai, Tamilnadu, India.

Boundary Value Problems

|March 15, 2021

Summary

This study uses mathematical modeling to analyze antiviral therapy for Hepatitis B virus (HBV) infection, providing a semi-analytical solution to understand liver cell and virus interactions. The research includes stability analysis and numerical simulations for HBV disease dynamics.

Keywords:

Antiviral therapy LHAM Mathematical modeling

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Published on: May 10, 2022

Area of Science:

Virology
Mathematical Biology
Hepatology

Background:

Hepatitis B virus (HBV) causes severe liver disease and shares retroviral characteristics.
Understanding HBV dynamics is crucial for developing effective antiviral therapies.
Mathematical modeling offers a powerful tool to analyze complex biological systems like viral infections.

Purpose of the Study:

To investigate the impact of antiviral therapy on Hepatitis B virus (HBV) infection using mathematical modeling.
To derive a semi-analytical solution for the nonlinear differential equation governing HBV-liver cell interactions.
To perform stability analysis of disease-free and endemic equilibria for HBV infection.

Main Methods:

Liao's homotopy analysis method (LHAM) was employed to obtain semi-analytical solutions.
Lyapunov functions were utilized for local and global stability analysis.
Mathematica 12 software was used for numerical simulations, graphical representations, and error analysis up to the sixth-order approximation.

Main Results:

A straightforward and direct semi-analytical solution was obtained using LHAM.
The stability of disease-free and endemic equilibrium points was rigorously analyzed.
Numerical simulations and error analysis provided insights into the behavior of HBV infection under antiviral therapy.

Conclusions:

Liao's homotopy analysis method is effective for solving nonlinear differential equations in viral dynamics.
The study provides a mathematical framework for understanding HBV infection and the efficacy of antiviral treatments.
The findings contribute to the development of more targeted and effective HBV therapies.