Vaccination and the theory of games

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.

Fig. 1.

Vaccine coverage p^* at the CSNE versus relative risk r, from Eq. 17, for various values of . Dashed horizontal lines demarcate the critical coverage level p_crit that eliminates the disease from the population (Eq. 12). In the limit of very large , the plot of p^* versus r approaches a step function with a step at r = 1 (Eq. 17).

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.

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.