The increasing occurrence of panic stampedes during mass events has motivated studying the impact of panic on crowd dynamics. Understanding the collective behaviors of panic stampedes is essential to reducing the risk of deadly crowd disasters. In this work, we use an agent-based formulation to model the collective human behavior in such crowd dynamics. We investigate the impact of panic behavior on crowd dynamics, as a specific form of collective behavior, by introducing a contagious panic parameter. The proposed model describes the intensity and spread of panic through the crowd. The corresponding panic parameter impacts each individual to represent a different variety of behaviors that can be associated with panic situations such as escaping danger, clustering, and pushing. Simulation results show contagious panic and pushing behavior, resulting in a more realistic crowd dynamics model.