Skip to main page content
U.S. flag

An official website of the United States government

Dot gov

The .gov means it’s official.
Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.

Https

The site is secure.
The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

Access keys NCBI Homepage MyNCBI Homepage Main Content Main Navigation
. 2004 Sep 7;101(36):13391-4.
doi: 10.1073/pnas.0403823101. Epub 2004 Aug 25.

Vaccination and the theory of games

Affiliations

Vaccination and the theory of games

Chris T Bauch et al. Proc Natl Acad Sci U S A. .

Abstract

Voluntary vaccination policies for childhood diseases present parents with a subtle challenge: if a sufficient proportion of the population is already immune, either naturally or by vaccination, then even the slightest risk associated with vaccination will outweigh the risk from infection. As a result, individual self-interest might preclude complete eradication of a vaccine-preventable disease. We show that a formal game theoretical analysis of this problem leads to new insights that help to explain human decision-making with respect to vaccination. Increases in perceived vaccine risk will tend to induce larger declines in vaccine uptake for pathogens that cause more secondary infections (such as measles and pertussis). After a vaccine scare, even if perceived vaccine risk is greatly reduced, it will be relatively difficult to restore prescare vaccine coverage levels.

PubMed Disclaimer

Figures

Fig. 1.
Fig. 1.
Vaccine coverage p* at the CSNE versus relative risk r, from Eq. 17, for various values of formula image. Dashed horizontal lines demarcate the critical coverage level pcrit that eliminates the disease from the population (Eq. 12). In the limit of very large formula image, the plot of p* versus r approaches a step function with a step at r = 1 (Eq. 17).
Fig. 2.
Fig. 2.
Analysis of vaccine scares: payoff gain, ΔE, and change in vaccine uptake, ΔP, after a shift in risk perception from r < π0 to r′ (see Table 1). For this figure, r = 0.1 and the proportion of individuals currently adopting the new CSNE is ε = 0 (corresponding to the start of a vaccine scare); the shapes of the curves are qualitatively similar for other values of r and ε.
Fig. 3.
Fig. 3.
Analysis of public education programs to counteract vaccine scares: payoff gain, ΔE, and change in vaccine uptake, ΔP, after a shift in risk perception from r > π0 to r′. As in Fig. 2, ε = 0 here. The results are independent of r (because the CSNE is always P = 0 when r > π0). The shapes of the curves are qualitatively similar for other values of ε, but the maximum of ΔE goes to zero as ε increases to 1.

References

    1. Durbach, N. (2000) Soc. Hist. Med. 13 (1), 45-62. - PubMed
    1. Albert, M. R., Ostheimer, K. G. & Breman, J. G. (2001) N. Engl. J. Med. 344, 375-379. - PubMed
    1. Streefland, P. H. (2001) Health Policy 55, 159-172. - PubMed
    1. Baker, J. P. (2003) Vaccine 21, 4003-4010. - PubMed
    1. Jansen, V. A. A., Stollenwerk, N., Jensen, H. J., Ramsay, M. E., Edmunds, W. J. & Rhodes, C. J. (2003) Science 301, 804. - PubMed

Publication types