Global dynamics of a diffusive viral infection model with general incidence function and distributed delays

Abstract

The distributed delay was firstly proposed by Volterra in the 1930s since it is more realistic than discrete delay and has been introduced in many dynamical systems. In this paper, we establish a diffusive viral infection model with general incidence function and distributed delays subject to the homogeneous Neumann boundary conditions. Firstly, we prove the existence, uniqueness, positivity and boundedness of solutions of the model. Then, by using the linearization method and constructing appropriate Lyapunov functionals, we show that the global dynamics of the model is determined by the reproductive numbers for viral infection $$\mathcal {R}_{0}$$ , which implies that the global stability of the model precludes the existence of complex dynamical behaviors such as Hopf bifurcation and patter formation. Furthermore, an example is presented and numerical simulations are also carried out to illustrate the main results.