Periodic solution of a stochastic HBV infection model with logistic hepatocyte growth

• A stochastic HBV model within logistic hepatocyte growth is developed.
• Existence of at least one periodic solution induced by white noise is shown.
• Existence of a unique stationary distribution is displayed.
• Results are supported numerically.

In this paper, we present a stochastic hepatitis B virus (HBV) infection model with logistic hepatocyte growth. We show that the stochastic differential equation (SDE) HBV model has at least one periodic solution induced by the white noise, and a unique stationary distribution which is stable. One of the most interesting findings is that random perturbations may be beneficial to format the periodic solution to the SDE HBV model.