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

TL;DR

This paper introduces a compartmental advection-diffusion model to analyze the spread of human behaviors like alertness, panic, and control during catastrophic events, supported by mathematical proofs and numerical simulations.

Contribution

It presents a novel macroscopic model for human behavior dynamics during disasters, with rigorous mathematical analysis and simulation-based insights.

Findings

Proved local existence, uniqueness, and regularity of the model solutions.

Demonstrated the propagation of behaviors through numerical simulations.

Provided insights into evacuation scenarios during catastrophic events.

Abstract

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.