Journal
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
Volume 31, Issue 6, Pages 1277-1295Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218202521400066
Keywords
Pedestrian flow models; disease spread models; multi-group macroscopic equations; particle methods
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Funding
- German research foundation, DFG [KL 1105/30-1]
- DAAD
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This paper investigates the impact of crowd motion in a complex dynamical environment on disease spreading, and proposes a kinetic equation for multi-group pedestrian flow based on a social force model coupled with an Eikonal equation. Simulation results indicate that the model accurately captures the dynamics of pedestrian flow and disease spread in different test cases.
Modeling and simulation of disease spreading in pedestrian crowds have recently become a topic of increasing relevance. In this paper, we consider the influence of the crowd motion in a complex dynamical environment on the course of infection of the pedestrians. To model the pedestrian dynamics, we consider a kinetic equation for multi-group pedestrian flow based on a social force model coupled with an Eikonal equation. This model is coupled with a non-local SEIS contagion model for disease spread, where besides the description of local contacts, the influence of contact times has also been modeled. Hydrodynamic approximations of the coupled system are derived. Finally, simulations of the hydrodynamic model are carried out using a mesh-free particle method. Different numerical test cases are investigated, including uni- and bi-directional flow in a passage with and without obstacles.
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