Dynamics on Hepatitis B Virus Infection In Vivo with Immune Noise and Interval Delay

Immune delay and noise are ubiquitous in the evolution of hepatitis B virus (HBV) infection in vivo . A stochastic HBV infection dynamic model is proposed to investigate the interaction effects of interval delay and white noise during the immune phase. Global existence, nonnegativity, and boundedness of the solutions are obtained. The stochastic reproduction number is derived, which serves as a threshold determining viral extinction or persistence within-host. Furthermore, the stability conditions for the first and second moments are established. Numerical simulations, employing time-series analysis, confirm the existence of stochastic periodicity. Compared to the deterministic model, noise induces an earlier onset of stochastic periodicity. However, based on the expectation stability of the sample trajectories, as the Hopf bifurcation of the corresponding deterministic system has not yet occurred, the noise-induced early periodicity is likely a temporary phenomenon rather than a true periodic behavior.