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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.
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.
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