Analysis of a spatio-temporal advection-diffusion model for human behaviors during a catastrophic event

In this work, using the theory of first-order macroscopic crowd models, we introduce a compartmental advection–diffusion model, describing the spatio-temporal dynamics of a population in different human behaviors (alert, panic and control) during a catastrophic event. For this model, we prove the local existence, uniqueness and regularity of a solution, as well as the positivity and $L^1$-boundedness of this solution. Then, in order to study the spatio-temporal propagation of these behavioral reactions within a population during a catastrophic event, we present several numerical simulations for different evacuation scenarios.