McGill researchers have found that dangerous crowd conditions leading to surges and stampedes may not emerge suddenly, but instead develop gradually, as repeated physical contact and pushing may accumulate and become synchronized among nearby individuals.
Recognizing how these conditions arise could help organizers strengthen security, site management and evacuation planning, reducing the likelihood of injuries during large-scale public events.
"In high-density settings such as concerts, sporting events or festivals, crowd crushes and stampedes can sometimes occur without obvious warning signs," said Shanwei Liu, a visiting PhD student in the Department of Civil Engineering and the study's lead author. "However, these incidents are often not truly 'sudden'; they may begin with small pushes between individuals and gradually escalate through ongoing interactions."
Highest-risk areas are near sides of exits, not in front of them
The study found that sustained physical contact drives a crowd's "emotion," causing people to imitate pushing behaviours. It also identified the highest-risk areas as being near the sides of exits, rather than directly in front of them, and developed an empirical formula to help planners estimate safer evacuation strategies.
The researchers suggest that crowd safety can be improved by targeting hidden high-risk zones, positioning staff strategically and using predictive models to manage pressure and capacity before dangerous surges emerge.
The team also recommended reducing prolonged body contact through spacing control, physical barriers and phased entry and exit strategies. They suggest intervening quickly as pressure builds, rather than only after people fall.
How instability spreads
Previous studies have focused on collision propagation in crowds, or on panic behaviours after accidents occur, Liu explained.
To better understand how risky conditions lead to tragedies, the team developed virtual crowd simulations using mathematical models of crowd behaviour. These models showed how individual pushing can lead people to unconsciously synchronize their movements into co-ordinated waves.
Unlike earlier approaches that treated people as static figures that fall like dominoes, the model represented them as unstable bodies trying to stay upright. This allowed the researchers to observe how instability spreads through a crowd: not only through falls, but through people struggling to maintain balance.
The model was tested under realistic, high‑density conditions, which helped the researchers understand how local interactions evolve into crowd surges, identify high‑risk zones and evaluate how factors such as layout and staffing influence safety.
Findings could be applied to other situations
As a next step, the researchers say they plan to study how rescue activities influence surrounding pedestrians during emergencies.
"In real incidents, rescue personnel often need to move against evacuation flows to reach dangerous areas, and these interactions may create new risks or affect crowd movement," Liu said. "We hope to better understand how rescue efforts and evacuations influence one another and explore safer management strategies."
The researchers said their findings could also have broader implications for policy and governance.
"We are interested in whether these types of nonlinear evolutionary mechanisms may share common patterns across different systems (socioeconomic, financial and political), where seemingly minor disruptions can potentially propagate into cascading or systemic failures," said Jiangbo Yu , an Assistant Professor in the Department of Civil Engineering and the study's corresponding author.
About this study
" Modeling and analyzing phantom crowd stampedes through emotion accumulation, behavioral synchronization, and collision propagation ," by Shanwei Liu, Yubo Jiao and Jiangbo Yu, was published in Chaos, Solitons & Fractals.
The research was funded by the Natural Sciences and Engineering Research Council of Canada and the China Scholarship Council.
