Abstract
In this manuscript, we study a model of human capital accumulation during the spread of disease following an agent-based approach, where agents behave maximising their intertemporal utility. We assume that the agent interaction is of mean field type, yielding a mean field game description of the problem. We discuss how the analysis of a model including both the mechanism of change of species from one epidemiological state to the other and an optimisation problem for each agent leads to an aggregate behaviour that is not easy to describe, and that sometimes exhibits structural issues. Therefore we eventually propose and study numerically a SEIRD model in which the rate of infection depends on the distribution of the population, given exogenously as the solution to the mean field game system arising as the macroscopic description of the discrete multi-agent economic model for the accumulation of human capital. Such a model arises in fact as a simplified but tractable version of the initial one.
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Acknowledgements
Daria Ghilli, Cristiano Ricci and Giovanni Zanco have been supported by the PRIN project “The Time-Space Evolution of Economic Activities: Mathematical Models and Empirical Applications”. Daria Ghilli and Cristiano Ricci have been supported by the INdAM-GNAMPA project “Modelli MFGs in Economia per lo studio della dinamica del capitale umano con spillovers spaziali”. Giovanni Zanco has been supported by the INdAM-GNAMPA projects “Sistemi con interazione spaziale: convergenza, controllo e applicazioni” and “Analisi qualitativa di PDE stocastiche: ergodicitá ed equazioni di Kolmogorov”.
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Ghilli, D., Ricci, C. & Zanco, G. A mean field game model for COVID-19 with human capital accumulation. Econ Theory 77, 533–560 (2024). https://doi.org/10.1007/s00199-023-01505-0
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DOI: https://doi.org/10.1007/s00199-023-01505-0