A nonconservative kinetic framework for a closed-market society subject to shock events

TL;DR

This paper develops a kinetic model for closed-market societies to analyze the impact of shock events like natural disasters, incorporating non-conservative interactions and external forces, with simulations and real-world application to Hurricane Katrina.

Contribution

It introduces a novel non-conservative kinetic framework with external shock modeling for societal dynamics, extending traditional conservative models.

Findings

Model captures differential impacts across income classes.

Simulations demonstrate shock effects on societal wealth distribution.

Application to Hurricane Katrina data validates the model's relevance.

Abstract

Recently, several events have shockingly impacted society, carrying tough consequences. However, not all individuals are similarly affected by shock events. Among other factors, the consequences can vary depending on the income class. In our presented work, the approach typical of kinetic theory is used to analyze the dynamics of a closed-market society exposed to various types of shock events. To achieve this, we introduce non-conservative equations, incorporating proliferative and destructive binary interactions as well as external actions. Specifically, the latter term reproduces the shock events, and to accomplish this, we introduce an appropriate external force field into the kinetic framework, modeled using Gaussian functions. Several numerical simulations are presented to illustrate the behavior of the solution predicted by the model and an application in comparison to real data relative to the Hurricane Katrina catastrophe is carried out.