Travelling waves of a hepatitis B virus infection model with spatial diffusion and time delay

Abstract

This paper is concerned with the existence of travelling waves to a hepatitis B virus infection with spatial diffusion in which the intracellular incubation period is modelled by a discrete time delay. By analyzing the corresponding characteristic equations, the local stability of an uninfected steady state and an infected steady state to this system under homogeneous Neumann boundary conditions is discussed. By using the cross-iteration method and the Schauder's fixed point theorem, we reduce the existence of travelling waves to the existence of a pair of upper-lower solutions. By constructing a pair of upper-lower solutions, we derive the existence of a travelling wave connecting the uninfected steady state and the infected steady state. Numerical simulations are carried out to illustrate the main results.