Computation of Macroscopic Density and Velocity from Microscopic Data for a Coupled People-Εpidemics Transport Process

We introduce an approach for derivation and smoothing of macroscopic densities and velocities from people trajectories, obtained from actual (microscopic) position data of individuals within a football stadium over a ninety-minute time horizon. In particular, we compute macroscopic densities for each type of individuals, who may belong to susceptible, infected, or exposed category. Our derivation approach relies on detection of exposed individuals based on derivation of critical contacts duration between susceptible and infected individuals. We then utilize kernel-based methods to compute smoothed versions of the densities/velocities derived, which enables assignment of density/velocity values throughout the spatial domain considered, despite the (spatial) sparsity of the trajectory data considered. Consequently, our approach could be useful for realistic calibration of macroscopic, coupled crowd flow – epidemics spreading models.