📝 SummarXiv

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.