We consider hyperbolic partial differential equations (PDEs) for a dynamic description of the traffic behavior in road networks. These equations are coupled to a Hawkes process that models traffic accidents taking into account their self-excitation property which means that accidents are more likely in areas in which another accident just occurred. We discuss how both model components interact and influence each other. A data analysis reveals the self-excitation property of accidents and determines further parameters. Numerical simulations using risk measures underline and conclude the discussion of traffic accident effects in our model.

翻译：我们考虑用双曲型偏微分方程（PDEs）对道路网络中的交通行为进行动态描述。这些方程与一个霍克斯过程相耦合，该过程在建模交通事故时考虑了事故的自激特性，即事故更可能发生在刚发生过其他事故的区域。我们讨论了这两个模型组成部分如何相互作用和相互影响。数据分析揭示了事故的自激特性，并确定了其他参数。使用风险度量的数值模拟强调并总结了模型中交通事故效应的讨论。