A KINETIC MODEL COUPLING CROWD MOVEMENT WITH INFECTIOUS DISEASE CONTAGION

AGNELLI JUAN PABLO; BUFFA, BRUNO ADOLFO; DAMIAN KNOPOFF; TORRES GERMAN

Congreso; 13th Conference on Dynamical Systems Applied to Biology and Natural Sciences ? DSABNS; 2022

We present a multiscale approach for the modeling of disease spreading and crowd movement in boundedenvironments during a short period of time. The model is based on the kinetic theory of active particles [2]and consider a system of interacting pedestrians, whose microscopic state is identified by their position andvelocity direction, as introduced in [1]. The first attempts to couple this model with disease contagion canbe found in [3, 4] for the 1D and 2D cases, respectively. In this new setting we add a microscopic variableaccounting for the individual state related to an infectious disease: namely, pedestrians can be either suscep-tible, exposed or infected. We will introduce the mathematical model and show how the transitions modeledat the microscopic level affect the macroscopic dynamics of the system. A qualitative analysis will be per-formed and some numerical simulations to study the sensitivity to model parameters and to understand howexposure to an infectious agent may promote disease spreading will be discussed.