In this paper, we study an SEIR model with both infection and latency ages and also a very general class of nonlinear incidence. We first present some preliminary results on the existence of solutions and on bounds of solutions. Then we study the global dynamics in detail. After proving the existence of a global attractor \(\mathcal{A}\), we characterize it in two cases distinguished by the basic reproduction number \(R_{0}\). When \(R_{0}<1\), we apply the Fluctuation Lemma to show that the disease-free equilibrium \(E_{0}\) is globally asymptotically stable, which means \(\mathcal{A}=\{E_{0}\}\). When \(R_{0}>1\), we show the uniform persistence and get \(\mathcal{A}=\{E_{0}\}\cup C \cup \mathcal{A}_{1}\), where \(C\) consists of points with connecting orbits from \(E_{0}\) to \(\mathcal{A}_{1}\) and \(\mathcal{A}_{1}\) attracts all points with initial infection force. Under an additional condition, we employ the approach of Lyapunov functional to find that \(\mathcal{A}_{1}\) just consists of an endemic equilibrium.

在本文中，我们研究了具有感染年龄和潜伏期的SEIR模型，以及一类非常普通的非线性发生率。我们首先介绍一些关于解决方案的存在性和解决方案范围的初步结果。然后，我们详细研究了全局动力学。在证明了全局吸引子\（\ mathcal {A} \）的存在之后，我们在两种情况下将其表征为基本复制数\（R_ {0} \）。当\（R_ {0} <1 \）时，我们应用涨落引理表明无病平衡\（E_ {0} \）在全局上是渐近稳定的，这意味着\（\ mathcal {A} = \ { E_ {0} \} \）。当\（R_ {0}> 1 \）时，我们显示统一的持久性并得到\（\ mathcal {A} = \ {E_ {0} \} \ cup C \ cup \ mathcal {A} _ {1} \），其中\（C \）由点与\（E_ { 0} \）到\（\ mathcal {A} _ {1} \）和\（\ mathcal {A} _ {1} \）会吸引具有初始感染力的所有点。在附加条件下，我们使用Lyapunov函数的方法来发现\（\ mathcal {A} _ {1} \）仅由地方均衡组成。