Analysis of a stochastic HBV infection model with delayed immune response

Considering the environmental factors and uncertainties, we propose, in this paper, a higherorder stochastically perturbed delay differential model for the dynamics of hepatitis B virus (HBV) infection with immune system. Existence and uniqueness of an ergodic stationary distribution of positive solution to the system are investigated, where the solution fluctuates around the endemic equilibrium of the deterministic model and leads to the stochastic persistence of the disease. Under some conditions, infection-free can be obtained in which the disease dies out exponentially with probability one. Some numerical simulations, by using Milstein's scheme, are carried out to show the effectiveness of the obtained results. The intensity of white noise plays an important role in the treatment of infectious diseases. Keywords: HBV; Lyapunov functional; Milstein's scheme; non-linear perturbations; stationary distribution and ergodicity; time-delays