The goal of this work is to study an infectious disease spreading in a medium size population occupying a confined environment. For this purpose, we consider a kinetic theory approach to model crowd dynamics in bounded domains and couple it to a kinetic equation to model contagion. The interactions of a person with other pedestrians and the environment are modeled by using tools of game theory. The pedestrian dynamics model allows to weight between two competing behaviors: the search for less congested areas and the tendency to follow the stream unconsciously in a panic situation. Each person in the system has a contagion level that is affected by the people in their neighborhood. For the numerical solution of the coupled problem, we propose a numerical algorithm that at every time step solves one crowd dynamics problem and one contagion problem, i.e. with no subiterations between the two. We test our coupled model on a problem involving a small crowd walking through a corridor.

中文翻译：

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有限环境中行人动力学与疾病传染的耦合动力学理论方法

这项工作的目标是研究一种传染病在占据封闭环境的中等规模人群中传播。为此，我们考虑了一种动力学理论方法来模拟有界域中的人群动力学，并将其耦合到动力学方程以模拟传染。使用博弈论工具对人与其他行人和环境的交互进行建模。行人动力学模型允许在两种竞争行为之间权衡：寻找不那么拥挤的区域和在恐慌情况下无意识地跟随溪流的趋势。系统中的每个人都有一个传染级别，该级别会受到附近居民的影响。对于耦合问题的数值解，我们提出了一种数值算法，该算法在每个时间步解决一个人群动力学问题和一个传染问题，即两者之间没有subiterations。我们在涉及一小群人穿过走廊的问题上测试我们的耦合模型。