期刊
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
卷 30, 期 10, 页码 1893-1915出版社
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218202520400126
关键词
Crowd dynamics; Boltzmann-type kinetic model; complex systems; contagion model
资金
- NSF [DMS-1620384]
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.
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