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

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.

References in corpus (5)

• Kinetic Exchange Models for Income and Wealth Distributions
• Wealth distribution under the spread of infectious diseases
• A nonconservative kinetic model under the action of an external force field for modeling the medical treatment of autoimmune response
• Reaction-diffusion systems derived from kinetic theory for Multiple Sclerosis
• A kinetic derivation of spatial distributed models for tumor-immune system interactions