Effects of Vaccination Efficacy on Wealth Distribution in Kinetic Epidemic Models

Emanuele Bernardi, Lorenzo Pareschi*, Giuseppe Toscani, Mattia Zanella

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)
15 Downloads (Pure)


The spread of the 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 modeling, 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.

Original languageEnglish
Article number216
Issue number2
Early online date29 Jan 2022
Publication statusPublished - Feb 2022


  • Compartmental epidemic modelling
  • COVID-19
  • Kinetic models
  • Vaccination campaign
  • Wealth distribution
  • Wealth inequalities

ASJC Scopus subject areas

  • Information Systems
  • Mathematical Physics
  • Physics and Astronomy (miscellaneous)
  • Electrical and Electronic Engineering


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