A modified social force model for sudden attack evacuation based on Yerkes–Dodson law and the tendency toward low risk areas

Various evacuation models are the internal support for the movement of pedestrians. Emergencies that occur in public places have the characteristics of suddenness, massive and unpredictability. These characteristics impact pedestrians’ psychological states, ultimately shaping their behaviors. However, the existing models do not fully consider this aspect. Therefore, for sudden attack events, based on the social force model and Yerkes–Dodson law, this paper proposes a modified model which considers the positive and negative effects of psychological state on pedestrians’ behaviors in three dimensions: the realization degree of desired speed, the proximity of attacker to pedestrian, and crowdedness. It also considers the diminishment of repulsion and the attractiveness of low risk areas. A behavioral model based on the exit-reorientation mechanism is proposed to describe the behavior of low risk exit selection according to the relative location of the attacker. The improved model is validated quantitatively and qualitatively, respectively. Simulations based on this model can effectively reproduce the behaviors of crowds in videos. The data of fundamental diagrams from our model fits well with that from videos. We find that the evacuation time is longer when the observation distance within a specific range in the simple scenario. The risk tolerance level of 8 m and 6 m are the critical points affecting the rate of change of survival rate and casualties, respectively. Simulation results indicate that the effect of rational people ratio on evacuation time will vary with risk tolerance level. This study offers insights into the dynamics of crowd evolution during an evacuation following a sudden attack, providing a foundation for exit allocation and emergency crowd guidance.