A mean field game model for COVID-19 with human capital accumulation

Daria Ghilli (), Cristiano Ricci () and Giovanni Zanco ()
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Daria Ghilli: Universitá di Pavia
Cristiano Ricci: Universitá di Pisa
Giovanni Zanco: Universitá di Siena

Economic Theory, 2024, vol. 77, issue 1, No 16, 533-560

Abstract: 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.

Keywords: Spatial SIR type models; Mean field games; Spatial interactions (search for similar items in EconPapers)
JEL-codes: C73 D90 E19 I10 O11 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s00199-023-01505-0

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