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Individual Vaccination as Nash Equilibrium in a SIR Model with Application to the 2009–2010 Influenza A(H1N1) Epidemic in France

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Laguzet_Turinici_vaccination.pdf (571.4Kb)
Date
2015
Publisher city
Paris
Dewey
Probabilités et mathématiques appliquées
Sujet
epidemic control; SIR model; individual vaccination; mean field games; vaccine scares; Nash equilibrium
Journal issue
Bulletin of mathematical biology
Volume
77
Number
10
Publication date
2015
Article pages
1955-1984
DOI
http://dx.doi.org/10.1007/s11538-015-0111-7
URI
https://basepub.dauphine.fr/handle/123456789/14509
Collections
  • CEREMADE : Publications
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Author
Laguzet, Laetitia
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Turinici, Gabriel
56663 Institut Universitaire de France [IUF]
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Type
Article accepté pour publication ou publié
Abstract (EN)
The vaccination against ongoing epidemics is seldom compulsory but remains one of the most classical means to fight epidemic propagation. However, recent debates concerning the innocuity of vaccines and their risk with respect to the risk of the epidemic itself lead to severe vaccination campaign failures, and new mass behaviors appeared driven by individual self-interest. Prompted by this context, we analyze, in a Susceptible–Infected–Recovered model, whether egocentric individuals can reach an equilibrium with the rest of the society. Using techniques from the “Mean Field Games” theory, we extend previous results and show that an equilibrium exists and characterizes completely the individual best vaccination strategy (with or without discounting). We also compare with a strategy based only on overall societal optimization and exhibit a situation with nonnegative price of anarchy. Finally, we apply the theory to the 2009–2010 Influenza A (H1N1) vaccination campaign in France and hint that a group of individuals stopped vaccinating at levels that indicated a pessimistic perception of the risk of the vaccine.

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