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.