Based on the fact that the incubation periods of epidemic disease in asymptomatically infected and infected individuals are inevitable and different, we propose a diffusive susceptible, asymptomatically infected, symptomatically infected and vaccinated (SAIV) epidemic model with delays in this paper. To see whether epidemic disease can propagate spatially with a constant speed, we focus on the travelling wave solution for this model. When the basic reproduction number of the corresponding spatial-homogenous delayed differential system is greater than one and the wave speed is greater than or equal to the critical speed, we prove that this model admits nontrivial positive travelling wave solutions. Our theoretical results are of benefit to the prevention and control of epidemic.

基于无症状感染者和感染者的流行病潜伏期不可避免且不同的事实，我们提出了一种具有延迟的扩散易感、无症状感染、有症状感染和已接种疫苗（SAIV）流行模型。为了了解流行病是否可以以恒定速度在空间传播，我们关注该模型的行波解。当相应的空间齐次延迟微分系统的基本再生数大于1且波速大于或等于临界速度时，我们证明了该模型允许非平凡的正行波解。我们的理论成果有利于疫情防控。