Every day, as you make your way to work, to the mall, to buy groceries, what is common? You find yourself interacting directly or indirectly with numerous other people. Although this may sound casual and not of much importance, sociologists, physicists, engineers, and mathematicians have been studying the behaviours of crowds of people for the past two decades.
Understanding crowd behaviour is the first step towards predicting and preventing crowd disasters like the Halloween stampede at Seoul, South Korea, in 2022, where 159 people were killed and 196 others were injured during a crowd rush for Halloween festivities. Understanding crowd behaviour is also important when it comes to planning of cities, including roads, and while designing public facilities like malls, schools, and metro stations, and implementing safety measures during any crowd event.
In this study by Dr. P. S. Abdul Salam, Prof. S. Tiwari, and Prof. A. Klar from the Department of Mathematics, TU Kaiserslautern, Kaiserslautern, Germany (Dr. P. S. Abdul Salam is also from the Centre for Computational Mathematics and Data Science, Department of Mathematics, Indian Institute of Technology Madras, Chennai, India), and Prof. S. Sundar from the Centre for Computational Mathematics and Data Science, Department of Mathematics, Indian Institute of Technology Madras, Chennai, India, fluid dynamic models have been developed to understand crowd behaviour in the presence of obstacles – both moving and stationary.
A microscopic pedestrian model based on social and behavioural forces was developed and a hydrodynamic model was mathematically derived from it. Equations were also developed to govern the movement of obstacles that interact with the pedestrians. The qualitative behaviour of the crowd when encountering obstacles while navigating their path towards an exit/target was also studied.
The collision avoidance behaviour of pedestrians gave insight into the way in which size, shape, position, and velocity of obstacles could affect the pedestrian flow and hence the evacuation efficiency from any closed domain. This knowledge is useful to implement safety regulations. The modelling framework can be extended to consider specific scenarios of pedestrian interaction with vehicular traffic.
The model developed in this study is also useful for disease models, such as the COVID-19 pandemic when social distancing was the norm.
To conclude, the modelling efforts of this study have proved to be adaptable to various geometries and scenarios replicating real life. The model was extended to vehicular traffic and disease contagion models. Future applications of this model could extend to autonomous vehicles (driverless cars) and robot navigation.
Prof. Dr. Thomas Goetz from the Mathematical Institute, University of Koblenz, Mainz, Germany, gave his analysis of the work done by the authors with the following comments: “Understanding the dynamics of human crowds in mass events like rock concerts, sports or religious events is a major key to prevent crowd disasters like in the Love Parade 2010 in Germany or during the Haij 2015 in Mecca, Saudi Arabia. Modeling and simulating the behavior of human crowds has been a hot topic in research over the past decades. Abdul Salam, Tiwari and co-workers present in their paper a microscopic model for pedestrian behavior. Analytical results are complemented by numerical simulations for crowds flowing around obstacles.”
Article by Akshay Anantharaman
Click here for the original link to the paper