Effects of vaccination efficacy on wealth distribution in kinetic epidemic models

TL;DR

This paper models how vaccination effectiveness influences wealth inequality during a pandemic by combining epidemic dynamics with kinetic wealth distribution models, showing vaccination reduces economic disparities.

Contribution

It introduces a novel kinetic model integrating epidemic spread and wealth exchange, demonstrating vaccination's role in mitigating economic inequality during pandemics.

Findings

Vaccination campaigns decrease wealth inequality.

Effective vaccination reduces economic disparities.

Mathematical equilibrium states show improved wealth distribution with vaccination.

Abstract

The spreading of Covid-19 pandemic has highlighted the close link between economics and health in the context of emergency management. A widespread vaccination campaign is considered the main tool to contain the economic consequences. This paper will focus, at the level of wealth distribution modelling, on the economic improvements induced by the vaccination campaign in terms of its effectiveness rate. The economic trend during the pandemic is evaluated resorting to a mathematical model joining a classical compartmental model including vaccinated individuals with a kinetic model of wealth distribution based on binary wealth exchanges. The interplay between wealth exchanges and the progress of the infectious disease is realized by assuming on the one hand that individuals in different compartments act differently in the economic process and on the other hand that the epidemic affects risk in economic transactions. Using the mathematical tools of kinetic theory, it is possible to identify the equilibrium states of the system and the formation of inequalities due to the pandemic in the wealth distribution of the population. Numerical experiments highlight the importance of the vaccination campaign and its positive effects in reducing economic inequalities in the multi-agent society.