Stochastic Dynamics of Hepatitis B Virus Infection: Analysis, Stability, and Numerical Simulation

TL;DR

This paper models hepatitis B virus infection dynamics using stochastic differential equations, analyzing stability, existence, and simulation results to understand the impact of randomness on infection outcomes.

Contribution

It introduces a stochastic model for HBV infection, proving solution properties and stability, and demonstrates how noise influences viral persistence or extinction.

Findings

Stochastic noise can lead to viral extinction even when deterministic models predict persistence.

The model establishes existence, uniqueness, and positivity of solutions for all relevant initial conditions.

Numerical simulations validate analytical results and show the stabilizing effect of environmental noise.

Abstract

This study develops and analyzes a stochastic differential equation (SDE) model for the dynamics of hepatitis B virus (HBV) infection. While deterministic frameworks have yielded important insights into viral behavior, they cannot adequately describe the intrinsic randomness and fluctuations present in biological processes. To address this limitation, we construct a stochastic model incorporating multiplicative environmental noise to account for variability in infection rates, cellular mortality, and viral replication. We establish a rigorous theoretical foundation by proving the existence, uniqueness, and global positivity of solutions for all biologically relevant initial conditions. Stability properties are investigated in detail, including stability in probability and almost sure exponential stability, with particular emphasis on conditions under which random perturbations stabilize the infection-free state. Furthermore, we demonstrate the existence of a unique ergodic stationary distribution and derive convergence properties of the uninfected hepatocyte population. Numerical simulations, performed via the Euler-Maruyama method with sufficiently small time steps to ensure positivity and accuracy, validate the analytical results and illustrate the impact of stochastic fluctuations on system dynamics. The simulations confirm that environmental noise can induce viral extinction even in parameter regimes where deterministic analysis predicts persistence. These findings enhance the mathematical understanding of HBV infection dynamics and underscore the significant role of stochastic effects in shaping long-term disease outcomes.