Global optimal vaccination in the SIR model: Properties of the value function and application to cost-effectiveness analysis

Mathematical Biosciences

Volumn 263, Issue , 2015, Pages 180-197

  Laguzet, Laetitia ^a   Turinici, Gabriel ^b  

^a UNIVERSITÉ PARIS DAUPHINE   (France)

^b INSTITUT UNIVERSITAIRE DE FRANCE   (France)

Author keywords

Herd immunity and cost effectiveness; Optimal vaccination; SIR model; Vaccination region

Indexed keywords

COST BENEFIT ANALYSIS; COST EFFECTIVENESS; COSTS; OPTIMAL CONTROL SYSTEMS;

COST EFFECTIVENESS ANALYSIS; GLOBAL OPTIMUM SOLUTIONS; HAMILTON-JACOBI-BELLMAN EQUATIONS; HERD IMMUNITIES; OPTIMAL VACCINATION; SIR MODEL; SUSCEPTIBLE-INFECTED-RECOVERED MODEL; VACCINATION REGION;

VACCINES;

PERTUSSIS VACCINE;

BACTERIAL DISEASE; COST ANALYSIS; IMMUNITY; VACCINATION; VACCINE;

ARTICLE; COMPARTMENT MODEL; COST EFFECTIVENESS ANALYSIS; DISEASE MODEL; HEALTH CARE POLICY; HERD IMMUNITY; HUMAN; MATHEMATICAL ANALYSIS; NONHUMAN; PERTUSSIS; PUBLIC HEALTH; QUALITY ADJUSTED LIFE YEAR; SUSCEPTIBLE INFECTED RECOVERED MODEL; UNSPECIFIED SIDE EFFECT; VACCINATION; COST BENEFIT ANALYSIS; MASS IMMUNIZATION; STANDARDS; THEORETICAL MODEL;

COST-BENEFIT ANALYSIS; HUMANS; IMMUNITY, HERD; MASS VACCINATION; MODELS, THEORETICAL;

EID: 84961301516     PISSN: 00255564     EISSN: 18793134     Source Type: Journal    
DOI: 10.1016/j.mbs.2015.03.002     Document Type: Article

References (33)

1. Abakuks A. Optimal immunisation policies for epidemics. Adv. Appl. Probab. 1974, 6:494-511.
2. Behncke H. Optimal control of deterministic epidemics. Optim. Control Appl. Methods 2000, 21(6):269-285. 10.1002/oca.678.
3. Morton R., Wickwire K.H. On the optimal control of a deterministic epidemic. Adv. Appl. Probab. 1974, 6:622-635.
4. Piunovskiy A.B., Clancy D. An explicit optimal intervention policy for a deterministic epidemic model. Optim. Control Appl. Methods 2008, 29(6):413-428. 10.1002/oca.834.
5. Anderson R.M., May R.M. Infectious Diseases of Humans Dynamics and Control 1992, Oxford University Press.
6. Diekmann O., Heesterbeek H.J. Mathematical Epidemiology of Infectious Diseases. Model building, analysis and interpretation 1999, Wiley Series in Mathematical and Computational Biology. Chichester: Wiley.
7. Anderson R.M., Hollingsworth T.D., Nokes D.J. Mathematical Models of Transmission and Control 2009, 2. Oxford University Press, doi: 10.1093/med/9780199218707.003.0041.
8. Bardi M., Capuzzo-Dolcetta I. Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations. Systems & Control: Foundations & Applications 1997, Birkhäuser Boston Inc., Boston, MA, doi: 10.1007/978-0-8176-4755-1.
9. Bressan A., Piccoli B. Introduction to the Mathematical Theory of Control, AIMS Series on Applied Mathematics, vol. 2 2007, 2. American Institute of Mathematical Sciences (AIMS), Springfield, MO.
10. Sethi S.P., Staats P.W. Optimal control of some simple deterministic epidemic models. J. Oper. Res. Soc. 1978, 29(2):129-136. 10.2307/3009792.
11. Hansen E., Day T. Optimal control of epidemics with limited resources. J. Math. Biol. 2011, 62(3):423-451. 10.1007/s00285-010-0341-0.
12. Funk S., Salathé M., Jansen V.A.A. Modelling the influence of human behaviour on the spread of infectious diseases: a review. J. R. Soc. Interface 2010, 7:1247-1256. 10.1098/rsif.2010.0142.
13. Bauch C.T. Imitation dynamics predict vaccinating behaviour. Proc. Biol. Sci. 2005, 272(1573):1669-1675.
14. Shim E., Chapman G.B., Townsend J.P., Galvani A.P. The influence of altruism on influenza vaccination decisions. J. R. Soc. Interface 2012, 9(74):2234-2243. 10.1098/rsif.2012.0115.
15. Abakuks A. Some optimal isolation and immunisation policies for epidemics (Ph.D. thesis) 1972, University of Sussex.
16. Hethcote H.W., Waltman P. Optimal vaccination schedules in a deterministic epidemic model. Math. Biosci. 1973, 18(3-4):365-381. 10.1016/0025-5564(73)90011-4.
17. Ledzewicz U., Schättler H. On optimal singular controls for a general SIR-model with vaccination and treatment. Discrete Contin. Dyn. Syst. 2011, Dynamical Systems, Differential Equations and Applications. 8th AIMS Conference, Suppl. vol. II:981-990.
18. Soner H.M. Optimal control with state-space constraint. I. SIAM J. Control Optim. 1986, 24(3):552-561. 10.1137/0324032.
19. Crandall M.G., Ishii H., Lions P.L. User's guide to viscosity solutions of second order partial differential equations. Bull. Am. Math. Soc. (N.S.) 1992, 27(1):1-67. 10.1090/S0273-0979-1992-00266-5.
20. Zeckhauser R., Shepard D. Where now for saving lives?. Law Contemp. Probl. 1976, 40:5-45.
21. Sassi F. Calculating QALYs, comparing QALY and DALY calculations. Health Policy Plan. 2006, 21(5):402-408. 10.1093/heapol/czl018.
22. Anand S., Hanson K. Disability-adjusted life years: a critical review. J. Health Econ. 1997, 16(6):685-702. 10.1016/S0167-6296(97)00005-2.
23. Murray C.J., Lopez A.D. Global mortality, disability, and the contribution of risk factors: global burden of disease study. Lancet 1997, 349(9063):1436-1442. 10.1016/S0140-6736(96)07495-8.
24. 1994, World Health Organization, Geneva. C.J.L. Murray, A.D. Lopez, W.H. Organization (Eds.).
25. Edejer T., Organization W.H. Making Choices in Health: WHO Guide to Cost-Effectiveness Analysis, vol. 1 2003, 1. World Health Organization.
26. Medicine (U.S.) I., Howson C.P., Fineberg H.V., Howe C.J. Adverse Effects of Pertussis and Rubella Vaccines: A Report of the Committee to Review the Adverse Consequences of Pertussis and Rubella Vaccines 1991, National Academy Press, Washington, D.C.
27. Lee G.M., Murphy T.V., Lett S., Cortese M.M., Kretsinger K., Schauer S., Lieu T.A. Cost effectiveness of pertussis vaccination in adults. Am. J. Prev. Med. 2006, 32:186-193. 10.1016/j.amepre.2006.10.016.
28. Anderson R., May R. Directly transmitted infections diseases: control by vaccination. Science 1982, 215(4536):1053-1060. 10.1126/science.7063839.
29. Hethcote H.W. The mathematics of infectious diseases. SIAM Rev. 2000, 42(4):599-653. 10.1137/S0036144500371907.
30. Shillcutt S.D., Walker D.G., Goodman C.A., Mills A.J. Cost effectiveness in low- and middle-income countries. PharmacoEconomics 2009, 27(11):903-917. 10.2165/10899580-000000000-00000.
31. Evans D.B., Lim S.S., Adam T., Edejer T.T.T. Evaluation of current strategies and future priorities for improving health in developing countries. Br. Med. J. 2005, 331(7530):1457-1461. 10.1136/bmj.38658.675243.94.
32. 2006, The World Bank, doi:10.1596/978-0-8213-6179-5. A. Mills, A.R. Measham, P. Musgrove, J.G. Breman, D.T. Jamison, D.B. Evans, P. Jha, M. Claeson, G. Alleyne (Eds.).
33. Barles G. Solutions de viscosité des équations de Hamilton-Jacobi. Mathématiques & Applications (Berlin) [Mathematics & Applications], vol. 17 1994, Springer-Verlag, Paris.