Issue |
Math. Model. Nat. Phenom.
Volume 15, 2020
Coronavirus: Scientific insights and societal aspects
|
|
---|---|---|
Article Number | 35 | |
Number of page(s) | 25 | |
DOI | https://doi.org/10.1051/mmnp/2020022 | |
Published online | 19 June 2020 |
- A. Abakuks, An optimal isolation policy for an epidemic. J. Appl. Prob. 10 (1973) 247–262. [Google Scholar]
- A. Abakuks, Optimal immunisation policies for epidemics. Adv. Appl. Prob. 6 (1974) 494–511. [Google Scholar]
- Y. Achdou and M. Laurière, Mean field type control with congestion. Appl. Math. Optim. 73 (2016) 393–418. [Google Scholar]
- L. Ambrosio, N. Gigli and G. Savaré, Gradient flows in metric spaces and in the space of probability measures, 2nd edn. Birkhäuser, Basel (2008). [Google Scholar]
- S. Anand and K. Hanson, Disability-adjusted life years: a critical review. J. Health Eco. 16 (1997) 685–702. [CrossRef] [Google Scholar]
- R.M. Anderson and R.M. May, Infectious Diseases of Humans Dynamics and Control. Oxford University Press, Oxford (1992). [Google Scholar]
- R.M. Anderson, T.D. Hollingsworth and D.J. Nokes, Mathematical models of transmission and control, Vol. 2. Oxford University Press, Oxford (2009). [Google Scholar]
- N. Bacaer, Un modéle mathématique des débuts de l’épidémie de coronavirus en France. MMNP 15 (2020) 29. [EDP Sciences] [Google Scholar]
- M. Bardi and I. Capuzzo-Dolcetta, Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations. Systems & Control: Foundations & Applications. Birkhäuser Boston Inc., Boston, MA (1997). [Google Scholar]
- C.T. Bauch and D.J.D. Earn, Vaccination and the theory of games. Proc. Natl. Acad. Sci. USA 101 (2004) 13391–13394. [CrossRef] [MathSciNet] [Google Scholar]
- H. Behncke, Optimal control of deterministic epidemics. Optim. Control Appl. Methods 21 (2000) 269–285. [Google Scholar]
- A. Bressan and F. Rampazzo, Impulsive control systems with commutative vector fields. J. Optim. Theory Appl. 71 (1991) 67–83. [Google Scholar]
- B. Buonomo, A. d’Onofrio and D. Lacitignola. Global stability of an SIR epidemic model with information dependent vaccination. Math. Biosci. 216 (2008) 9–16. [Google Scholar]
- V. Capasso, Mathematical Structures of Epidemic Systems. Lecture Notes in Biomathematics. Springer-Verlag, Berlin (1993). [CrossRef] [Google Scholar]
- V. Capasso and G. Serio, A generalization of the Kermack-McKendrick deterministic epidemic model. Math. Biosci. 42 (1978) 43–61. [Google Scholar]
- R. Carmona, J.P. Fouque and L.H. Sun, Mean field games and systemic risk. Commun. Math. Sci. 13 (2015) 911–933. [Google Scholar]
- R. Carmona, F. Delarue, et al. Probabilistic Theory of Mean Field Games with Applications I-II. Springer, Berlin (2018). [Google Scholar]
- G. Dal Maso and F. Rampazzo, On systems of ordinary differential equations with measures as controls. Differ. Integral Equ. 4 (1991) 739–765. [Google Scholar]
- A. Danchin, T.W.P. Ng and G. Turinici, A new transmission route for the propagation of the SARS-CoV-2 coronavirus. Preprint medRxiv: 20022939v1 (2020). [Google Scholar]
- R. Djidjou-Demasse, Y. Michalakis, M. Choisy, M.T. Sofonea and S. Alizon, Optimal COVID-19 epidemic control until vaccine deployment. Preprint medRxiv: 20049189v3 (2020). [Google Scholar]
- J. Dolbeault and G. Turinici, Heterogeneous social interactions and the COVID-19 lockdown outcome in a multi-group SEIR model. Preprint arXiv:2005.00049 (2020). [Google Scholar]
- A. d’Onofrio, P. Manfredi and E. Salinelli, Vaccinating behaviour, information, and the dynamics of SIR vaccine preventable diseases. Theor. Popul. Biol. 71 (2007) 301–317. [PubMed] [Google Scholar]
- A. d’Onofrio, P. Manfredi and E. Salinelli. Fatal SIR diseases and rational exemption to vaccination. Math. Med. Biol. 25 (2008) 337–357. [Google Scholar]
- R. Elie, E. Hubert, T. Mastrolia and D. Possamaï, Mean-field moral hazard for optimal energy demand response management. Preprint arXiv:1902.10405 (2019). [Google Scholar]
- R. Élie, T. Ichiba and M. Laurière, Large banking systems with default and recovery: A mean field game model. Preprint arXiv:2001.10206 (2020). [Google Scholar]
- E.P. Fenichel, C. Castillo-Chavez, M.G. Ceddia, G. Chowell, P.A.G. Parra, G.J. Hickling, G. Holloway, R. Horan, B. Morin, C. Perrings, M. Springbornh, L. Velazqueze and C. Villalobos, Adaptive human behavior in epidemiological models. Proc. Natl. Acad. Sci. 108 (2011) 6306–6311. [CrossRef] [Google Scholar]
- S. Ghader, J. Zhao, M. Lee, W. Zhou, G. Zhao, L. Zhang, Observed mobility behavior data reveal social distancing inertia. Preprint arXiv:2004.14748 (2020). [Google Scholar]
- O. Guéant, J.-M. Lasry and P.-L. Lions, Mean field games and applications, in Paris-Princeton lectures on mathematical finance 2010. Springer, Berlin (2011) 205–266. [CrossRef] [Google Scholar]
- E. Hansen and T. Day, Optimal control of epidemics with limited resources. J. Math. Biol. 62 (2011) 423–451. [Google Scholar]
- M. Huang, R. Malhamé and P. Caines, Large population stochastic dynamic games: Closed–loop McKean–Vlasov systems and the Nash certainty equivalence principle. Commun. Inf. Syst. 6 (2006) 221–252. [Google Scholar]
- M. Huang, P. Caines and R. Malhamé, An invariance principle in large population stochastic dynamic games. J. Syst. Sci. Complex. 20 (2007) 162–172. [Google Scholar]
- M. Huang, P. Caines and R. Malhamé, Large–population cost–coupled LQG problems with nonuniform agents: Individual–mass behavior and decentralized ε–Nash equilibria. IEEE Trans. Auto. Control 52 (2007) 1560–1571. [Google Scholar]
- M. Huang, P. Caines and R. Malhamé, The Nash certainty equivalence principle and McKean–Vlasov systems: An invariance principle and entry adaptation, in 46th IEEE Conference on Decision and Control (2007) 121–126. [Google Scholar]
- E. Hubert and G. Turinici, Nash-MFG equilibrium in a SIR model with time dependent newborn vaccination. Ric. Mat. 67 (2018) 227–246. [CrossRef] [Google Scholar]
- L. Laguzet and G. Turinici, Global optimal vaccination in the SIR model: properties of the value function and application to cost-effectiveness analysis. Math. Biosci. 263 (2015) 180–197. [Google Scholar]
- 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. Bull. Math. Biol. 77 (2015) 1955–1984. [Google Scholar]
- L. Laguzet, G. Turinici and G. Yahiaoui, Equilibrium in an individual-societal SIR vaccination model in presence of discounting and finite vaccination capacity, in New Trends in Differential Equations, Control Theory and Optimization: Proceedings of the 8th Congress of Romanian Mathematicians (2016) 201–214. [CrossRef] [Google Scholar]
- J.-M. Lasry and P.-L. Lions, Jeux à champ moyen. I–Le cas stationnaire. C R Math. 343 (2006) 619–625. [Google Scholar]
- J.-M. Lasry and P.-L. Lions, Jeux à champ moyen. II–Horizon fini et contrôle optimal. C R Math. 343 (2006) 679–684. [Google Scholar]
- J.-M. Lasry and P.-L. Lions, Mean field games. Jpn. J. Math. 2 (2007) 229–260. [CrossRef] [MathSciNet] [Google Scholar]
- S. Lenhart and J.T. Workman, Optimal control applied to biological models. CRC Press, Boca Raton (2007). [CrossRef] [Google Scholar]
- Q. Li, X. Guan, P. Wu, X. Wang, L. Zhou, Y. Tong, R. Ren, K.S.M. Leung, E.H.Y. Lau, J.Y. Wong, X. Xing, N. Xiang, Y. Wu, C. Li, Q. Chen, D. Li, T. Liu, J. Zhao, M. Liu, W. Tu, C. Chen, L. Jin, R. Yang, Q. Wang, S. Zhou, R. Wang, H. Liu, Y. Luo, Y. Liu, G. Shao, H. Li, Z. Tao, Y. Yang, Z. Deng, B. Liu, Z. Ma, Y. Zhang, G. Shi, T.T.Y. Lam, J.T. Wu, G.F. Gao, B.J. Cowling, B. Yang, G.M. Leung and Z. Feng, Early Transmission Dynamics in Wuhan, China, of Novel Coronavirus-Infected Pneumonia. New Engl. J. Med. 382 (2020) 1199–1207. [Google Scholar]
- R. Morton and K.H. Wickwire, On the optimal control of a deterministic epidemic. Adv. Appl. Prob. 6 (1974) 622–635. [CrossRef] [Google Scholar]
- T. Ng, G. Turinici and A. Danchin, A double epidemic model for the SARS propagation. BMC Infect. Dis. 3 (2003) 19. [Google Scholar]
- A. Perasso, An introduction to the basic reproduction number in mathematical epidemiology. ESAIM: Proc. Surv. 62 (2018) 123–138. [CrossRef] [Google Scholar]
- A.B. Piunovskiy and D. Clancy, An explicit optimal intervention policy for a deterministic epidemic model. Optim. Control Appl. Methods 29 (2008) 413–428. [Google Scholar]
- A.S. Poznyak, Topics of functional analysis, in Advanced Mathematical Tools for Automatic Control Engineers: Deterministic Techniques, edited by A.S. Poznyak. Elsevier, Oxford (2008) 451–498. [CrossRef] [Google Scholar]
- A. Rizzo, M. Frasca, M. Porfiri, Effect of individual behavior on epidemic spreading in activity-driven networks. Phys. Rev. E 90 (2014) 042801. [Google Scholar]
- F.D. Sahneh, F.N. Chowdhury and C.M. Scoglio, On the existence of a threshold for preventive behavioral responses to suppress epidemic spreading. Sci. Rep. 2 (2012) 632. [CrossRef] [PubMed] [Google Scholar]
- F. Salvarani and G. Turinici, Optimal individual strategies for influenza vaccines with imperfect efficacy and durability of protection. Math. Biosci. Eng. 15 (2018) 629. [CrossRef] [PubMed] [Google Scholar]
- F. Sassi, Calculating QALYs, comparing QALY and DALY calculations. Health Policy Plan. 21 (2006) 402–408. [CrossRef] [PubMed] [Google Scholar]
- S.P. Sethi and P.W. Staats, Optimal control of some simple deterministic epidemic models. Oper. Res. Soc. J. 29 (1978) 129–136. [CrossRef] [Google Scholar]
- G. Silva and R. Vinter, Necessary conditions for optimal impulsive control problems. SIAM J. Control Optim. 35 (1997) 1829–1846. [Google Scholar]
- G. Turinici, Metric gradient flows with state dependent functionals: The Nash-MFG equilibrium flows and their numerical schemes. Nonlinear Anal. 165 (2017) 163–181. [CrossRef] [Google Scholar]
- G. Turinici and A. Danchin, The SARS Case Study: An Alarm Clock? in Encyclopedia of Infectious Diseases. John Wiley & Sons, Ltd, New Jersey (2006) 151–162. [Google Scholar]
- V. Volpert, M. Banerjee, A. d’Onofrio, T. Lipniacki, S. Petrovskii and V.C. Tran, Coronavirus: scientific insights and societal aspects. MMNP 15 (2020) E2. [EDP Sciences] [Google Scholar]
- Z. Wang, C.T. Bauch, S. Bhattacharyya, A. d’Onofrio, P. Manfredi, M. Perc, N. Perra, M. Salathé and D. Zhao, Statistical physics of vaccination. Phys. Rep. 664 (2016) 1–113. [Google Scholar]
- K. Wickwire, Optimal isolation policies for deterministic and stochastic epidemics. Math. Biosci. 26 (1975) 325–346. [Google Scholar]
- R. Zeckhauser and D. Shepard, Where now for saving lives. Law Contemp. Probl. 40 (1976) 5. [Google Scholar]
- E. Zeidler, Applied Functional Analysis: Applications to Mathematical Physics. Applied Mathematical Sciences. Springer, New York (2012). [Google Scholar]
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.