In this paper, for a class of nonlocal dispersal SIR epidemic models with nonlinear incidence, we study the existence of traveling waves connecting the disease-free equilibrium with endemic equilibrium. We obtain that the existence of traveling waves depends on the minimal wave speed \(c^{*}\) and basic reproduction number \(\mathcal{R}_{0}\). That is, if \(\mathcal{R}_{0}>1\) and \(c> c^{*}\) then the model has a traveling wave connecting the disease-free equilibrium with endemic equilibrium. Otherwise, if \(\mathcal{R}_{0}>1\) and \(0< c< c^{*}\), then there does not exist the traveling wave connecting the disease-free equilibrium with endemic equilibrium. The numerical simulations verify the theoretical results. Our results improve and generalize some known results.

在本文中，对于一类具有非线性发病率的非局部分散 SIR 流行模型，我们研究了连接无病平衡和地方病平衡的行波的存在。我们得到行波的存在取决于最小波速\(c^{*}\)和基本再生数\(\mathcal{R}_{0}\)。也就是说，如果\(\mathcal{R}_{0}>1\)和\(c> c^{*}\)那么该模型具有连接无病平衡和地方病平衡的行波。否则，如果\(\mathcal{R}_{0}>1\)和\(0< c< c^{*}\)，则不存在连接无病平衡与地方病平衡的行波。数值模拟验证了理论结果。我们的结果改进并概括了一些已知的结果。