疾病传染人群动力学模型的动力学理论方法
A kinetic theory approach to model crowd dynamics with disease contagion
摘要：
我们提出了一些想法，如何扩展的动力学类型的人群动力学模型，以考虑传染病的传播。我们专注于一个中等规模的人群占据了一个封闭的环境，疾病很容易传播。我们选择的动力论方法使用对策论的工具来模拟一个人与周围的人和环境的相互作用，它的特点是一个参数来代表压力的水平。众所周知，人们在受到恐惧或压力的情况下会选择不同的行走策略。为了证明我们的人群动力学模型可以用来再现现实的场景，我们模拟乘客在休斯顿的霍比机场的一个终端。为了模拟疾病在步行人群中的传播，我们引入了一个变量，表示接触传播疾病的人的水平。此外，我们引入了一个参数，描述了传染相互作用的强度和核函数，这是一个减函数之间的距离的人和一个传播的个人。我们测试我们的传染模型的一个问题，涉及一小群人走过走廊。
英文摘要：
We present some ideas on how to extend a kinetic type model for crowd dynamics to account for an infectious disease spreading. We focus on a medium size crowd occupying a confined environment where the disease is easily spread. The kinetic theory approach we choose uses tools of game theory to model the interactions of a person with the surrounding people and the environment and it features a parameter to represent the level of stress. It is known that people choose different walking strategies when subjected to fear or stressful situations. To demonstrate that our model for crowd dynamics could be used to reproduce realistic scenarios, we simulate passengers in one terminal of Hobby Airport in Houston. In order to model disease spreading in a walking crowd, we introduce a variable that denotes the level of exposure to people spreading the disease. In addition, we introduce a parameter that describes the contagion interaction strength and a kernel function that is a decreasing function of the distance between a person and a spreading individual. We test our contagion model on a problem involving a small crowd walking through a corridor.
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