A Microscopic Approach to Pedestrian Dynamics and the Onset of Disease Spreading

In this dissertation we analyze the numerical results of a microscopic approach that models pedestrian dynamics.

Firstly, we focus on a space-continuous model that represents pedestrian dynamics by the forces acting on them. We consider that each pedestrian is driven by the desire to reach a certain target and is influenced by the space geometry as well as by the pedestrians surrounding them. These forces on the pedestrians are modeled using Newton's second law of dynamics as a guiding principle. The model results in a high-dimensional system of second order ordinary differential equations. The time evolution of the positions and velocities of all pedestrians is then obtained by numerical integration.

The various parameters in our model are numerically calibrated for a simple straight corridor and their significance to the model is analyzed. A major side effect of spatially continuous models are oscillations and overlaps. They are also analyzed in a quantitative manner for the same corridor.

Next, we validate our model through a serious of experiments. We compute the evacuation time from a room with varying exit door size. Our results are compared to the numerical results obtained for the same experiment using a kinetic theory approach. We notice that our model had a higher rate of decrease of evacuation times compared to the kinetic model. Then, we validate our model by comparing with empirical results. We compare the average velocity against the mean density of a group of people passing through a particular portion of a corridor. Our results are in good agreement with the empirical ones. Finally, we show that our model can reproduce self-organization of the pedestrians. We consider a bidirectional flow of pedestrians in a corridor and successfully observe that our model reproduces lane formation without explicitly setting the model to do so.

Lastly, we combine our pedestrian dynamics model with a contact tracking model to compute the average number of people getting infected by sick people inside airports.