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

Recently, several events have shockingly impacted society, carrying tough consequences. This was evident in the recent COVID-19 pandemic. However, not all individuals are affected by shock events in the same way. Among other factors, the consequences can vary depending on the wealth 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 exploring different scenarios are presented to illustrate the behavior of the solution predicted by the model and to gain some insights when complex situations are investigated.