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

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.

💡 Research Summary

The paper introduces a novel non‑conservative kinetic framework to study how shock events—such as pandemics, wars, or natural disasters—affect wealth distribution and population dynamics in a closed‑market society. Traditional kinetic models of wealth exchange assume conservation of the number of agents and total wealth, which precludes the representation of external disturbances that cause migration, death, or sudden wealth loss. To overcome this limitation, the authors augment the classical discrete kinetic equations with two types of non‑conservative terms: (i) a proliferative/destructive interaction rate μ_{hk}(t) that modulates birth‑death‑like processes during binary encounters, and (ii) an external force field λ_i(t) that directly acts on each wealth class i, modeling the impact of a shock. The external field is chosen as a Gaussian function of time, λ_i(t)=α_i exp