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

Abstract

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