Spatial patterns caused by the intracellular time delay in a super‐diffusive HBV model with logistic hepatocyte growth

Abstract

A super‐diffusive HBV model with the intracellular time delay and logistic hepatocyte growth is studied. We discuss the local asymptotic stability of the unique positive equilibrium and prove that the intracellular time delay can cause spatial patterns. Furthermore, we find that system undergoes a Hopf bifurcation when the time delay increase to a critical value. By the normal form theory and the center manifold theorem, we investigate the stability and direction of the bifurcating periodic solutions. Finally, we present how the initial condition, time delay, superdiffusion coefficient and the exponent of superdiffusion affect spatial patterns by numerical simulations.