An optimal isolation policy for an epidemic, Journal of Applied Probability, vol.10, issue.2, pp.247-262, 1973. ,
Optimal immunisation policies for epidemics, Advances in Applied Probability, vol.6, pp.494-511, 1974. ,
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
Gradient flows in metric spaces and in the space of probability measures, 2008. ,
Disability-adjusted life years: a critical review, Journal of health economics, vol.16, issue.6, 1997. ,
Mathematical models of transmission and control, vol.2, 2009. ,
Infectious Diseases of Humans Dynamics and Control, 1992. ,
Un modèle mathématique des débuts de l'épidémie de coronavirus en France, Mathematical Modelling of Natural Phenomena, vol.15, p.29, 2020. ,
Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations, Systems & Control: Foundations & Applications, 1997. ,
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. ,
Optimal control of deterministic epidemics, Optimal Control Applications & Methods, vol.21, issue.6, pp.269-285, 2000. ,
Impulsive control systems with commutative vector fields, Journal of Optimization Theory and Applications, vol.71, issue.1, pp.67-83, 1991. ,
Global stability of an SIR epidemic model with information dependent vaccination, Mathematical Biosciences, vol.216, issue.1, pp.9-16, 2008. ,
Mathematical Structures of Epidemic Systems, Lecture Notes in Biomathematics, 1993. ,
A generalization of the Kermack-McKendrick deterministic epidemic model, Mathematical Biosciences, vol.42, issue.1, pp.43-61, 1978. ,
Probabilistic Theory of Mean Field Games with Applications I-II, 2018. ,
Mean field games and systemic risk, Communications in Mathematical Sciences, vol.13, issue.4, pp.911-933, 2015. ,
On systems of ordinary differential equations with measures as controls, Differential and Integral Equations, vol.4, issue.4, pp.739-765, 1991. ,
A new transmission route for the propagation of the SARS-CoV-2 coronavirus. medRxiv, 2020. ,
Optimal COVID-19 epidemic control until vaccine deployment. medRxiv, 2020. ,
URL : https://hal.archives-ouvertes.fr/hal-02533223
Heterogeneous social interactions and the COVID-19 lockdown outcome in a multi-group SEIR model, 2020. ,
URL : https://hal.archives-ouvertes.fr/hal-02559938
Fatal SIR diseases and rational exemption to vaccination, Mathematical Medicine and Biology, vol.25, issue.4, pp.337-357, 2008. ,
Vaccinating behaviour, information, and the dynamics of SIR vaccine preventable diseases, Theoretical Population Biology, vol.71, issue.3, pp.301-317, 2007. ,
Mean-field moral hazard for optimal energy demand response management, 2019. ,
, Large banking systems with default and recovery: A mean field game model, 2020.
Adaptive human behavior in epidemiological models, Proceedings of the National Academy of Sciences, vol.108, issue.15, pp.6306-6311, 2011. ,
, Observed mobility behavior data reveal social distancing inertia, 2020.
Mean field games and applications, Paris-Princeton lectures on mathematical finance 2010, pp.205-266, 2011. ,
Optimal control of epidemics with limited resources, Journal of Mathematical Biology, vol.62, issue.3, pp.423-451, 2011. ,
An invariance principle in large population stochastic dynamic games, Journal of Systems Science and Complexity, vol.20, issue.2, pp.162-172, 2007. ,
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. ,
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. ,
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. ,
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
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
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. ,
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
Jeuxà champ moyen. I-Le cas stationnaire, Comptes Rendus Mathématique, vol.343, issue.9, pp.619-625, 2006. ,
Jeuxà champ moyen. II-Horizon fini et contrôle optimal, Comptes Rendus Mathématique, vol.343, issue.10, pp.679-684, 2006. ,
Mean field games, Japanese Journal of Mathematics, vol.2, issue.1, pp.229-260, 2007. ,
URL : https://hal.archives-ouvertes.fr/hal-00667356
Optimal control applied to biological models, 2007. ,
, of Novel Coronavirus-Infected Pneumonia, 2020.
On the optimal control of a deterministic epidemic, Advances in Applied Probability, vol.6, issue.4, pp.622-635, 1974. ,
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
An introduction to the basic reproduction number in mathematical epidemiology, ESAIM: Proceedings and Surveys, vol.62, pp.123-138, 2018. ,
An explicit optimal intervention policy for a deterministic epidemic model, Optimal Control Applications & Methods, vol.29, issue.6, pp.413-428, 2008. ,
Chapter 18 -Topics of functional analysis, Advanced Mathematical Tools for Automatic Control Engineers: Deterministic Techniques, pp.451-498, 2008. ,
Effect of individual behavior on epidemic spreading in activity-driven networks, Physical Review E, vol.90, issue.4, p.42801, 2014. ,
On the existence of a threshold for preventive behavioral responses to suppress epidemic spreading, Scientific reports, vol.2, p.632, 2012. ,
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
Calculating QALYs, comparing QALY and DALY calculations. Health policy and planning, vol.21, pp.402-408, 2006. ,
Optimal control of some simple deterministic epidemic models, Operational Research Society Journal, vol.29, issue.2, pp.129-136, 1978. ,
Necessary conditions for optimal impulsive control problems, SIAM Journal on Control and Optimization, vol.35, issue.6, pp.1829-1846, 1997. ,
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
The SARS Case Study: An Alarm Clock?, Encyclopedia of Infectious Diseases, pp.151-162, 2006. ,
URL : https://hal.archives-ouvertes.fr/hal-00536581
Coronavirus: scientific insights and societal aspects, Mathematical Modelling of Natural Phenomena, 2020. ,
Statistical physics of vaccination, Physics Reports, vol.664, pp.1-113, 2016. ,
URL : https://hal.archives-ouvertes.fr/hal-01597313
Optimal isolation policies for deterministic and stochastic epidemics, Mathematical biosciences, vol.26, issue.3-4, pp.325-346, 1975. ,
Where now for saving lives, Law and Contemporary Problems, vol.40, issue.5, 1976. ,
Applied Functional Analysis: Applications to Mathematical Physics, Applied Mathematical Sciences, 2012. ,