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.

分布式延迟最早是由Volterra在1930年代提出的，因为它比离散延迟更现实，并且已在许多动力学系统中引入。在本文中，我们建立了具有一般入射函数和服从均匀Neumann边界条件的分布时滞的扩散病毒感染模型。首先，我们证明了模型解的存在性，唯一性，正性和有界性。然后，通过使用线性化方法并构建适当的Lyapunov函数，我们证明了该模型的全局动力学由病毒感染的生殖数\（\ mathcal {R} _ {0} \）决定，这意味着该模型的全局稳定性排除了诸如Hopf分叉和模式形成之类的复杂动力学行为的存在。此外，给出了一个例子，并进行了数值模拟以说明主要结果。