Stationary distribution of a reaction-diffusion hepatitis B virus infection model driven by the Ornstein-Uhlenbeck process

A reaction-diffusion hepatitis B virus (HBV) infection model based on the mean-reverting Ornstein-Uhlenbeck process is studied in this paper. We demonstrate the existence and uniqueness of the positive solution by constructing the Lyapunov function. The adequate conditions for the solution’s stationary distribution were described. Last but not least, the numerical simulation demonstrated that reversion rates and noise intensity influenced the disease and that there was a stationary distribution. It was concluded that the solution tends more toward the stationary distribution, the greater the reversion rates and the smaller the noise.