Dynamic equilibria of group vaccination strategies in a heterogeneous population

Journal of Global Optimization

Volumn 40, Issue 1-3, 2008, Pages 51-63

  Cojocaru, Monica Gabriela ^a  

^a UNIVERSITY OF GUELPH   (Canada)

Author keywords

Evolutionary variational inequalities; Population dynamics; Vaccination strategies

Indexed keywords

APPROXIMATION THEORY; DYNAMIC MODELS; GAME THEORY; POPULATION DYNAMICS; RISK ASSESSMENT;

EVOLUTIONARY VARIATIONAL INEQUALITIES (EVI); VACCINATION STRATEGIES;

VARIATIONAL TECHNIQUES;

EID: 38849143980     PISSN: 09255001     EISSN: 15732916     Source Type: Journal    
DOI: 10.1007/s10898-007-9204-7     Document Type: Conference Paper

References (35)

1. Albert M.R., Ostheimer K.G. and Breman J.G. (2001). The last smallpox epidemic in Boston and the vaccination controversy, 1901-1903. N. Engl. J. Med. 344: 375-379
2. Anderson R.M. and May R.M. (1991). Infectious Diseases of Humans. Oxford University Press, Oxford
3. Baiocchim, C., Capello, A.: Variational and Quasivariational Inequalities. Applications to Free Boundary Problems. J. Wiley and Sons (1984)
4. Bauch C.T. and Earn D.J.D. (2004). Vaccination and the theory of games. Proc. Natl. Acad. Sci. 101: 13391-13394
5. Bauch C.T. (2005). Imitation dynamics predict vaccinating behaviour. Proc. R. Soc. Lond. B 272: 1669-1675
6. Bensoussan A. (1974). Points des Nash dans le cas de fonctionelles quadratique et jeux differentiels lineaires a N-personnes. SIAM J. Control 12: 460-499
7. Bensoussan A. and Lions J.L. (1973). Nouvelle formulation de problemes de controle impulsionnel et applications. Comptes Rendus des Seances de l'Academie des Sciences 276: 1189-1192
8. Bensoussan A., Goursat M. and Lions J.L. (1973). Controle impulsionnel et innequations quasi-variationnelles stationnaires. Comptes Rendus des Seances de l'Academie des Sciences 276: 1279-1284
9. Biroscak B., Fiore A., Fasano N., Fineis P., Collins M. and Stoltman G. (2003). Impact of the thimerosal controversy on hepatitis B vaccine coverage of infants born to women of unknown hepatitis B surface antigen status in Michigan. Pediatrics 111: e645-e649
10. Brezis, H.: Inequations D'Evolution Abstraites. Comptes Rendue d'Academie des Sciences (1967)
11. Chapman G.B. and Coups E.J. (1999). Predictors of influenza vaccine acceptance among healthy adults. Preventitive Medicine 29: 249-262
12. Cojocaru, M.-G.: Piecewise solutions of evolutionary variational inequalities. Consequences for double-layered dynamics modelling of equilibrium problems. J. Ineq. Pure Appl. Math. (to appear in) (2007)
13. Cojocaru M.-G., Bauch C., Johnston M. (2007) Dynamics of vaccination strategies via projected dynamical systems. Bull. Mathemat. Biol. 69(5):1453-1476
14. Cojocaru M.-G., Daniele P. and Nagurney A. (2005). Projected dynamical systems and evolutionary variational inequalities via Hilbert spaces and applications. J. Optim. Theory Appl. 127(3): 549-563
15. Cojocaru M.-G., Daniele P., Nagurney A. (2006) Double-layer dynamics: a unified theory of projected dynamical systems and evolutionary variational inequalities. Eur. J. Operat. Res. 175(1):494-507
16. Cojocaru, M.-G., Daniele, P., Nagurney, A.: Projected dynamical systems, evolutionary variational inequalities, applications, and a computational procedure. In: Migdalos, A., Pardalos, P., Pitsoulis, L. (eds.) Pareto Optimality Game Theory and Equilibria. Nonconvex Optimization and its Applications Series, Springer (2006)
17. Cournot A.A. (1838). Researches into the Mathematical Principles of the Theory of Wealth, English translation 1897. MacMillan, London, England
18. Daniele P., Maugeri A. and Oettli W. (1999). Time-dependent traffic equilibria. J. Optim. Theory Appl. 103: 543-554
19. Daniele, P.: Dynamic Networks and Evolutionary Variational Inequalities. Edward Elgar Publishing (2006)
20. Durbach N. (2000). They might as well brand us: working class resistance to compulsory vaccination in Victorian England. Soc. Hist. Med. 13(1): 45-62
21. Fine P.E.M. and Clarkson J.A. (1986). Individual versus public priorities in the determination of optimal vaccination policies. Am. J. Epidem. 124: 1012-1020
22. Gabay, D., Moulin, H.: On the uniqueness and stbility of Nash-equilibria in noncooperative games. In: Applied Stochastic Control in Econometrics and Management Science, North Holland, Amsterdam (1980)
23. Gangarosa E.J., Galazka A.M., Wolfe C.R., Phillips L.M., Gangarosa R.E., Miller E. and Chen R.T. (1998). Impact of anti-vaccine movements on pertussis control: the untold story. Lancet 351: 356-361
24. Geoffard P.Y. and Philipson T. (1997). Disease eradication: Private versus public vaccination. Am. Econ. Rev. 87: 222-230
25. Goldstein K.P., Philipson T.J., Joo H. and Daum R.S. (1996). The effect of epidemic measles on immunization rates. JAMA 276: 56-58
26. Harker, P.T.: A variational inequality approach for the determination of oligopolistic market equilibrium (1984)
27. Harker P.T. (1991). Generalized Nash games and quasivariational inequalities. Eur. J. Operat. Res. 54: 81-94
28. Kinderlehrer, D., Stampacchia, G.: An Introduction to Variational Inequalities and Their Applications. Academic Press (1980)
29. Lashuay N., Tjoa T., de Nuncio M.L.Z., Franklin M., Elder J. and Jones M. (2000). Exposure to immunization media messages among African American parents. Prev. Med. 31: 522-528
30. Lions J.P. and Stampacchia G. (1967). Variational inequalities. Communi. Pure Appl. Mathemat. 20: 493-519
31. Maugeri, A., Vitanza, C.: Time-dependent equilibrium problems. In: Chinchuluun, A., Migdalas, A., Pardalos, P.M., Pitsoulis, L. (eds.) Pareto Optimality Game Theory and Equilibria, pp. 505-524. Nonconvex Optimization and its Applications Series, Springer (2006)
32. Nash J.F. (1950). Equilibrium points in n-person games. Proc. Nat. Acad. Sci. USA 36: 48-49
33. Nash J.F. (1951). Noncooperative games. Ann. Mathemat. 54: 286-298
34. Plotkin S. (2002). Lessons learned concerning vaccine safety. Vaccine 20(Suppl. 1): S16-S19
35. Poland G. and Jacobsen R. (2001). Understanding those who do not understand: a brief review of the anti-vaccine movement. Vaccine 19: 2440-2445