Stochastic dynamics on HBV infection in vivo with interval delay

Because noise is ubiquitous within-host, a stochastic dynamical system with interval delay is proposed to model the dynamics of HBV infection in vivo. The global existence and nonnegativity of the solutions are established. Virus extinction conditions are derived, under which the asymptotic properties of the virus-free equilibrium are proved, and the persistence conditions are obtained. Finally, numerical simulations are performed to examine the influence of noise on the Hopf bifurcation resulting from the delay parameters in the interval delay.