Individual vaccination as Nash equilibrium in a SIR model with application to the 2009-10 Influenza A(H1N1) epidemic in France - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Bulletin of Mathematical Biology Année : 2015

Individual vaccination as Nash equilibrium in a SIR model with application to the 2009-10 Influenza A(H1N1) epidemic in France

Résumé

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 (SIR) 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 non-negative 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.
Fichier principal
Vignette du fichier
Laguzet_Turinici_vaccination.pdf (566.1 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01100579 , version 1 (06-01-2015)
hal-01100579 , version 2 (15-06-2015)
hal-01100579 , version 3 (18-09-2015)

Identifiants

Citer

Laetitia Laguzet, Gabriel Turinici. Individual vaccination as Nash equilibrium in a SIR model with application to the 2009-10 Influenza A(H1N1) epidemic in France. Bulletin of Mathematical Biology, 2015, 77 (10), pp.1955-1984. ⟨10.1007/s11538-015-0111-7⟩. ⟨hal-01100579v3⟩
810 Consultations
1519 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More