A. Abakuks, An optimal isolation policy for an epidemic, Journal of Applied Probability, vol.10, issue.2, pp.247-262, 1973.

A. Abakuks, Optimal immunisation policies for epidemics, Advances in Applied Probability, vol.6, pp.494-511, 1974.

Y. Achdou and M. Laurière, Mean field type control with congestion, Applied Mathematics & Optimization, vol.73, issue.3, pp.393-418, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01139389

L. Ambrosio, N. Gigli, and G. Savaré, Gradient flows in metric spaces and in the space of probability measures, 2008.

S. Anand and K. Hanson, Disability-adjusted life years: a critical review, Journal of health economics, vol.16, issue.6, 1997.

R. M. Anderson, T. D. Hollingsworth, and D. J. Nokes, Mathematical models of transmission and control, vol.2, 2009.

R. M. Anderson and R. M. May, Infectious Diseases of Humans Dynamics and Control, 1992.

N. Bacaër, Un modèle mathématique des débuts de l'épidémie de coronavirus en France, Mathematical Modelling of Natural Phenomena, vol.15, p.29, 2020.

M. Bardi and I. Capuzzo-dolcetta, Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations, Systems & Control: Foundations & Applications, 1997.

C. T. Bauch and D. J. Earn, Vaccination and the theory of games, Proceedings of the National Academy of Sciences of the United States of America, vol.101, issue.36, pp.13391-13394, 2004.

H. Behncke, Optimal control of deterministic epidemics, Optimal Control Applications & Methods, vol.21, issue.6, pp.269-285, 2000.

A. Bressan and F. Rampazzo, Impulsive control systems with commutative vector fields, Journal of Optimization Theory and Applications, vol.71, issue.1, pp.67-83, 1991.

B. Buonomo, A. Onofrio, and D. Lacitignola, Global stability of an SIR epidemic model with information dependent vaccination, Mathematical Biosciences, vol.216, issue.1, pp.9-16, 2008.

V. Capasso, Mathematical Structures of Epidemic Systems, Lecture Notes in Biomathematics, 1993.

V. Capasso and G. Serio, A generalization of the Kermack-McKendrick deterministic epidemic model, Mathematical Biosciences, vol.42, issue.1, pp.43-61, 1978.

R. Carmona and F. Delarue, Probabilistic Theory of Mean Field Games with Applications I-II, 2018.

R. Carmona, J. P. Fouque, and L. H. Sun, Mean field games and systemic risk, Communications in Mathematical Sciences, vol.13, issue.4, pp.911-933, 2015.

G. Maso and F. Rampazzo, On systems of ordinary differential equations with measures as controls, Differential and Integral Equations, vol.4, issue.4, pp.739-765, 1991.

A. Danchin, T. W. Ng, and G. Turinici, A new transmission route for the propagation of the SARS-CoV-2 coronavirus. medRxiv, 2020.

R. Djidjou-demasse, Y. Michalakis, M. Choisy, M. T. Sofonea, and S. Alizon, Optimal COVID-19 epidemic control until vaccine deployment. medRxiv, 2020.
URL : https://hal.archives-ouvertes.fr/hal-02533223

J. Dolbeault and G. Turinici, Heterogeneous social interactions and the COVID-19 lockdown outcome in a multi-group SEIR model, 2020.
URL : https://hal.archives-ouvertes.fr/hal-02559938

A. Onofrio, P. Manfredi, and E. Salinelli, Fatal SIR diseases and rational exemption to vaccination, Mathematical Medicine and Biology, vol.25, issue.4, pp.337-357, 2008.

A. Onofrio, P. Manfredi, and E. Salinelli, Vaccinating behaviour, information, and the dynamics of SIR vaccine preventable diseases, Theoretical Population Biology, vol.71, issue.3, pp.301-317, 2007.

R. Elie, E. Hubert, T. Mastrolia, and D. Possamaï, Mean-field moral hazard for optimal energy demand response management, 2019.

R. Élie, T. Ichiba, and M. Laurière, Large banking systems with default and recovery: A mean field game model, 2020.

E. P. Fenichel, C. Castillo-chavez, M. G. Ceddia, G. Chowell, P. A. Parra et al., Adaptive human behavior in epidemiological models, Proceedings of the National Academy of Sciences, vol.108, issue.15, pp.6306-6311, 2011.

S. Ghader, J. Zhao, M. Lee, W. Zhou, G. Zhao et al., Observed mobility behavior data reveal social distancing inertia, 2020.

O. Guéant, J. Lasry, and P. Lions, Mean field games and applications, Paris-Princeton lectures on mathematical finance 2010, pp.205-266, 2011.

E. Hansen and T. Day, Optimal control of epidemics with limited resources, Journal of Mathematical Biology, vol.62, issue.3, pp.423-451, 2011.

M. Huang, P. Caines, and R. Malhamé, An invariance principle in large population stochastic dynamic games, Journal of Systems Science and Complexity, vol.20, issue.2, pp.162-172, 2007.

M. Huang, P. Caines, and R. Malhamé, Large-population cost-coupled LQG problems with nonuniform agents: Individualmass behavior and decentralized ?-Nash equilibria, IEEE Transactions on Automatic Control, vol.52, issue.9, pp.1560-1571, 2007.

M. Huang, P. Caines, and R. Malhamé, The Nash certainty equivalence principle and McKean-Vlasov systems: An invariance principle and entry adaptation, 46th IEEE Conference on Decision and Control, pp.121-126, 2007.

M. Huang, R. Malhamé, and P. Caines, Large population stochastic dynamic games: Closed-loop McKean-Vlasov systems and the Nash certainty equivalence principle, Communications in Information & Systems, vol.6, issue.3, pp.221-252, 2006.

E. Hubert and G. Turinici, Nash-MFG equilibrium in a SIR model with time dependent newborn vaccination, Ricerche di Matematica, vol.67, issue.1, pp.227-246, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01389584

L. Laguzet and G. Turinici, Global optimal vaccination in the SIR model: properties of the value function and application to cost-effectiveness analysis, Mathematical biosciences, vol.263, pp.180-197, 2015.
URL : https://hal.archives-ouvertes.fr/hal-00966622

L. Laguzet and G. Turinici, Individual Vaccination as Nash Equilibrium in a SIR Model with Application to the 2009-2010 Influenza A (H1N1) Epidemic in France, Bulletin of Mathematical Biology, vol.77, issue.10, pp.1955-1984, 2015.

L. Laguzet, G. Turinici, and G. Yahiaoui, Equilibrium in an individual-societal SIR vaccination model in presence of discounting and finite vaccination capacity, New Trends in Differential Equations, Control Theory and Optimization: Proceedings of the 8th Congress of Romanian Mathematicians, pp.201-214, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01222450

J. Lasry and P. Lions, Jeuxà champ moyen. I-Le cas stationnaire, Comptes Rendus Mathématique, vol.343, issue.9, pp.619-625, 2006.

J. Lasry and P. Lions, Jeuxà champ moyen. II-Horizon fini et contrôle optimal, Comptes Rendus Mathématique, vol.343, issue.10, pp.679-684, 2006.

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

S. Lenhart and J. T. Workman, Optimal control applied to biological models, 2007.

Q. Li, X. Guan, P. Wu, X. Wang, L. Zhou et al., of Novel Coronavirus-Infected Pneumonia, 2020.

R. Morton and K. H. Wickwire, On the optimal control of a deterministic epidemic, Advances in Applied Probability, vol.6, issue.4, pp.622-635, 1974.

T. Ng, G. Turinici, and A. Danchin, A double epidemic model for the SARS propagation, BMC Infectious Diseases, vol.3, issue.1, p.19, 2003.
URL : https://hal.archives-ouvertes.fr/hal-00784487

A. Perasso, An introduction to the basic reproduction number in mathematical epidemiology, ESAIM: Proceedings and Surveys, vol.62, pp.123-138, 2018.

A. B. Piunovskiy and D. Clancy, An explicit optimal intervention policy for a deterministic epidemic model, Optimal Control Applications & Methods, vol.29, issue.6, pp.413-428, 2008.

A. S. Poznyak, Chapter 18 -Topics of functional analysis, Advanced Mathematical Tools for Automatic Control Engineers: Deterministic Techniques, pp.451-498, 2008.

A. Rizzo, M. Frasca, and M. Porfiri, Effect of individual behavior on epidemic spreading in activity-driven networks, Physical Review E, vol.90, issue.4, p.42801, 2014.

F. D. Sahneh, F. N. Chowdhury, and C. M. Scoglio, On the existence of a threshold for preventive behavioral responses to suppress epidemic spreading, Scientific reports, vol.2, p.632, 2012.

F. Salvarani and G. Turinici, Optimal individual strategies for influenza vaccines with imperfect efficacy and durability of protection, Mathematical Biosciences & Engineering, vol.15, issue.3, p.629, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01302557

F. Sassi, Calculating QALYs, comparing QALY and DALY calculations. Health policy and planning, vol.21, pp.402-408, 2006.

S. P. Sethi and P. W. Staats, Optimal control of some simple deterministic epidemic models, Operational Research Society Journal, vol.29, issue.2, pp.129-136, 1978.

G. Silva and R. Vinter, Necessary conditions for optimal impulsive control problems, SIAM Journal on Control and Optimization, vol.35, issue.6, pp.1829-1846, 1997.

G. Turinici, Metric gradient flows with state dependent functionals: The Nash-MFG equilibrium flows and their numerical schemes, Nonlinear Analysis, vol.165, pp.163-181, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01528480

G. Turinici and A. Danchin, The SARS Case Study: An Alarm Clock?, Encyclopedia of Infectious Diseases, pp.151-162, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00536581

V. Volpert, M. Banerjee, A. Onofrio, T. Lipniacki, S. Petrovskii et al., Coronavirus: scientific insights and societal aspects, Mathematical Modelling of Natural Phenomena, 2020.

Z. Wang, C. T. Bauch, S. Bhattacharyya, A. Onofrio, P. Manfredi et al., Statistical physics of vaccination, Physics Reports, vol.664, pp.1-113, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01597313

K. Wickwire, Optimal isolation policies for deterministic and stochastic epidemics, Mathematical biosciences, vol.26, issue.3-4, pp.325-346, 1975.

R. Zeckhauser and D. Shepard, Where now for saving lives, Law and Contemporary Problems, vol.40, issue.5, 1976.

E. Zeidler, Applied Functional Analysis: Applications to Mathematical Physics, Applied Mathematical Sciences, 2012.