In this paper, we are concerned with existence/non-existence of traveling waves of a diffusive SIR epidemic model with general incidence rate of the form of $f\left(S\right)g\left(I\right)$ and infinitely distributed latency but without demography. We show that the existence of traveling waves only depends on the basic reproduction number of the corresponding spatial-homogeneous system of delay differential equations, which is determined by the recovery rate, the local properties of $f$ and $g$ and a minimal wave speed $c^{\ast }$ that is affected by the distributed delay. The proof of existence of traveling waves is by employing Schauder’s fixed point theorem, and the proof of nonexistence is completed with the aid of the bilateral Laplace transform.

在本文中，我们关注的是扩散SIR流行病模型的行波的存在/不存在，其总发生率为 $F（\mathrm{小号}）G（\mathrm{一世}）$和无限分布的延迟，但没有人口统计学。我们表明行波的存在仅取决于相应的时滞微分方程的空间齐次系统的基本重现数，该基本重现数由恢复率，重合子的局部性质确定。$F$ 和 $G$ 和最小的波速 $C^{\ast }$受分布式延迟的影响。行波存在的证明是通过使用Schauder不动点定理，而不存在的证明是通过双边拉普拉斯变换完成的。