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Coupling Pedestrian Flow and Disease Contagion Models

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Crowd Dynamics, Volume 4

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Abstract

Modeling and simulation of disease spreading in pedestrian crowds recently gained increasing relevance. We review an approach from Abdul Salam et al. describing the influence of the crowd motion in a complex dynamical environment on the course of infection of the pedestrians. Additionally, we discuss in this manuscript possible extensions and amplifications. In particular, we reconsider the definition of the non-local infection rate, which is crucial for the coupling of pedestrian motion and disease spreading. To model the dynamics of the pedestrians, a kinetic equation for multi-group pedestrian flow based on a social force model coupled with an Eikonal equation is used. This model is coupled to a non-local SEIS contagion model for disease spread. We discuss different models for the infection rate. Besides the modelling of the influence of the number of contacts and contact duration on the spreading of the disease, the influence of the spreading of an aerosol cloud is modelled via a drift-diffusion model coupled to the pedestrian motion. Finally, hydrodynamic approximations of the coupled system are derived and simulations of the hydrodynamic model are carried out using a mesh-free particle method. Different numerical test cases are investigated. From a geometrical point of view we concentrate on uni- and bi-directional flow in a passage with and without obstacles. We investigate situations with a homogeneous flow, as well as a pedestrian crowd at rest and situations with alternating periods of slow and fast movement. The numerical results indicate that, it is important for the description of the disease spread to take into account a realistic model for the contact time. In particular in situations with periods of slow motion or a crowd at rest, a model including contact time duration and models for the spreading of the aerosol cloud are necessary to obtain reliable results. We also find, that for flows with an obstacle or bottleneck, the number of exposed pedestrians is considerably increased due to the denser pedestrian crowd surrounding the obstacle. In general, the numerical results show the importance of the geometry of the domain for the rate of infection.

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Acknowledgements

This work is supported by DFG grant KL 1105/30-1, by BMBF grant HYDAMO and by a DAAD grant for Bi-nationally supervised doctoral degrees.

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Authors and Affiliations

  1. Department of Mathematics, IIT Madras, Chennai, India

    Parveena Shamim Abdul Salam

  2. Department of Mathematics, TU Kaiserslautern, Kaiserslautern, Germany

    Wolfgang Bock, Axel Klar & Sudarshan Tiwari

Authors
  1. Parveena Shamim Abdul Salam
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  2. Wolfgang Bock
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  3. Axel Klar
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  4. Sudarshan Tiwari
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Corresponding author

Correspondence to Axel Klar .

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Editors and Affiliations

  1. Department of Applied Mathematics, University of Granada, Granada, Spain

    Nicola Bellomo

  2. Institute for Multiscale Thermofluids, University of Edinburgh, Edinburgh, UK

    Livio Gibelli

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Abdul Salam, P.S., Bock, W., Klar, A., Tiwari, S. (2023). Coupling Pedestrian Flow and Disease Contagion Models. In: Bellomo, N., Gibelli, L. (eds) Crowd Dynamics, Volume 4. Modeling and Simulation in Science, Engineering and Technology. Birkhäuser, Cham. https://doi.org/10.1007/978-3-031-46359-4_9

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