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PreprintCC BY 4.0arXiv

A PDE-Based Model of Runner Flow in Mass Participation Events

  • Alice Molinari
  • Brian Block
  • Stephanie Stockar
  • Simona Sacone
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Abstract

This paper presents a macroscopic approach for modeling pedestrian movement. A convection-diffusion partial differential equation (PDE) is described and used to model the flow of runners along a marathon course. A marathon is a good modeling case study for human movement because the location of runners is only known in sparse locations, so an accurate model is needed to know where people are at all times. As well, marathons offer many safety and logistical problems that can be solved by modeling human movement. Data is obtained from the 2023 Columbus Marathon, and model improvements are made to include a temporally varying convection term. Results show an increase in model accuracy which can allow for better resource allocation and safety measures.

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Cite

BibTeXRIS
BibTeX
@misc{molinari2026pdebased,
  title = {{A PDE-Based Model of Runner Flow in Mass Participation Events}},
  author = {Alice Molinari and Brian Block and Stephanie Stockar and Simona Sacone},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.35206},
  eprint = {2610.35206},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.35206},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - A PDE-Based Model of Runner Flow in Mass Participation Events
AU  - Alice Molinari
AU  - Brian Block
AU  - Stephanie Stockar
AU  - Simona Sacone
PY  - 2026
DA  - 2026/10/26
PB  - arXiv
DO  - 10.48550/arxiv.2610.35206
UR  - https://arxiv.org/abs/2610.35206
AB  - This paper presents a macroscopic approach for modeling pedestrian movement. A convection-diffusion partial differential equation (PDE) is described and used to model the flow of runners along a marathon course. A marathon is a good modeling case study for human movement because the location of runners is only known in sparse locations, so an accurate model is needed to know where people are at all times. As well, marathons offer many safety and logistical problems that can be solved by modeling human movement. Data is obtained from the 2023 Columbus Marathon, and model improvements are made to include a temporally varying convection term. Results show an increase in model accuracy which can allow for better resource allocation and safety measures.
ER  -