W. O. Kermack and A. G. Mckendrick, A contribution to the mathematical theory of epidemics, Proceedings of the Royal Society of London A: mathematical, physical and engineering sciences, vol.115, pp.700-721, 1927.

P. J. Francis, Optimal tax/subsidy combinations for the flu season, Journal of Economic Dynamics and Control, vol.28, issue.10, pp.2037-2054, 2004.

L. Laguzet and G. Turinici, Individual vaccination as Nash equilibrium in a SIR model: the interplay between individual optimization and societal policies, 2015.

J. Doncel, N. Gast, and B. Gaujal, Discrete Mean Field Games: Existence of Equilibria and Convergence, Journal of Dynamics and Games, vol.6, issue.3, pp.1-19, 2019.
URL : https://hal.archives-ouvertes.fr/hal-01277098

D. A. Gomes, J. Mohr, and R. R. Souza, Discrete time, finite state space mean field games, Journal de Mathématiques Pures et Appliquées, vol.93, issue.3, pp.308-328, 2010.

L. F. Harko, T. , and M. M. , Exact analytical solutions of the susceptible-infectedrecovered (sir) epidemic model and of the sir model with equal death and birth rate, Applied Mathematics and Computation, issue.236, p.184194, 2014.

J. Doncel, N. Gast, and B. Gaujal, A Mean-Field Game Analysis of SIR Dynamics with Vaccination, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01496885

J. Lasry and P. Lions, Mean field games, Japanese Journal of Mathematics, vol.2, issue.1, pp.229-260, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00667356

H. Behncke, Optimal control of deterministic epidemics, Optimal control applications and methods, vol.21, issue.6, pp.269-285, 2000.