Imitation dynamics predict vaccinating behaviour

Proceedings of the Royal Society B: Biological Sciences - Tập 272 Số 1573 - Trang 1669-1675 - 2005
Chris T. Bauch1
1Department of Mathematics and Statistics, University of Guelph, Guelph, Ontario, Canada N1G 2W1

Tóm tắt

There exists an interplay between vaccine coverage, disease prevalence and the vaccinating behaviour of individuals. Moreover, because of herd immunity, there is also a strategic interaction between individuals when they are deciding whether or not to vaccinate, because the probability that an individual becomes infected depends upon how many other individuals are vaccinated. To understand this potentially complex interplay, a game dynamic model is developed in which individuals adopt strategies according to an imitation dynamic (a learning process), and base vaccination decisions on disease prevalence and perceived risks of vaccines and disease. The model predicts that oscillations in vaccine uptake are more likely in populations where individuals imitate others more readily or where vaccinating behaviour is more sensitive to changes in disease prevalence. Oscillations are also more likely when the perceived risk of vaccines is high. The model reproduces salient features of the time evolution of vaccine uptake and disease prevalence during the whole-cell pertussis vaccine scare in England and Wales during the 1970s. This suggests that using game theoretical models to predict, and even manage, the population dynamics of vaccinating behaviour may be feasible.

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Tài liệu tham khảo

Afzal M, 2000, Clinical safety issues of measles, mumps and rubella vaccines, Bull. WHO, 78, 199

10.1056/NEJM200102013440511

Anderson R.M& May R.M Infectious diseases of humans. 1991 Oxford University Press.

10.1016/S0264-410X(02)00702-8

10.1177/0272989X9401400204

10.1016/S0264-410X(03)00302-5

Bartlett M.S, 1956, Deterministic and stochastic models for recurrent epidemics, Proc. Third Berkeley Symp. Math. Stat. Probab, 4, 81

10.1073/pnas.0403823101

10.1098/rspb.2003.2410

10.1073/pnas.1731324100

10.1136/bmj.327.7417.725

10.1542/peds.111.6.e645

Bjoernerstedt J, 1996, The rational foundations of economic behaviour, 155

Bonanni P, 1998, Demographic impact of vaccination: a review, Vaccine, 17, S120

10.1007/BF00178328

Brauer F, 2003, Some directions for mathematical epidemiology, Fields Inst. Commun, 36, 95

10.1177/0272989X02239651

CDC, 2004, Progress toward poliomyelitis eradication—Nigeria, January 2003–March 2004, MMWR Wkly, 53, 343

10.1017/S0140525X03000050

Cullen J& West P The economics of health. An introduction. 1979 Oxford:Martin Robertson.

10.1001/jama.285.9.1183

10.1093/shm/13.1.45

10.1126/science.287.5453.667

Evans M, 2001, Parents' perspectives on the MMR immunisation: a focus group study, Br. J. Gen. Pract, 51, 904

Fenner F Henderson D Arita I Jezek Z& Ladnyi I Smallpox and its eradication. 1998 Geneva:World Health Organization.

10.1093/oxfordjournals.aje.a114471

10.1016/S0140-6736(97)04334-1

Geoffard P, 1997, Disease eradication: private versus public vaccination, Am. Econ. Rev, 87, 222

10.1038/414716a

Health Canada Division of immunization and respiratory diseases FAQ. 2004 http://www.hc-sc.gc.ca/pphb-dgspsp/dird-dimr/vs-sv.

Helbing D, 1992, Economic evolution and demographic change. Formal models in social sciences, 330, 10.1007/978-3-642-48808-5_18

Hethcote H.W, 2000, The mathematics of infectious diseases, Soc. Ind. Appl. Math. Rev, 42, 599

10.1007/s002850050003

Hofbauer J& Sigmund K Evolutionary games and population dynamics. 1998 Cambridge University Press.

10.1126/science.1086726

10.1126/science.275.5296.65

Kuznetsov Y Content: a multiplatform environment for continuation and bifurcation analysis of dynamical systems. 1999 http://www.enm.bris.ac.uk/staff/hinke/dss/continuation/content.html.

10.1006/pmed.2000.0745

10.1098/rspb.2001.1599

10.1056/NEJMoa021134

Maynard-Smith J Evolution and the theory of games. 1982 Cambridge University Press.

Miller E, 1997, Epidemiological determinants of pertussis, Dev. Biol. Stand, 89, 15

10.1136/bmj.316.7133.715

Plotkin S, 2002, Lessons learned concerning vaccine safety, Vaccine, 20, S16

10.1016/S0264-410X(00)00469-2

10.1136/bmj.310.6995.1629

10.1086/339467

10.1093/imammb/1.2.169

Schmitt H.J, 2002, Factors influencing vaccine uptake in Germany, Vaccine, 20, S2

10.1046/j.1365-2214.2003.00347.x

10.1038/18913

von Neumann J& Morgenstern O Theory of games and economic behavior. 1944 Princeton University Press.

Weibull J Evolutionary game theory. 1995 Cambridge MA:The MIT Press.

WHO Immunization vaccines and biologicals. 2004 http://www.who.int/vaccinessurveillance/statsandgraphs.htm.

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Proceedings of the Royal Society B: Biological Sciences

Tập 272 Số 1573

1669-1675

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