Evolutionary game theory and social learning can determine how vaccine scares unfold

Abstract

Immunization programs have often been impeded by vaccine scares, as evidenced by the measles-mumps-rubella (MMR) autism vaccine scare in Britain. A "free rider" effect may be partly responsible: vaccine-generated herd immunity can reduce disease incidence to such low levels that real or imagined vaccine risks appear large in comparison, causing individuals to cease vaccinating. This implies a feedback loop between disease prevalence and strategic individual vaccinating behavior. Here, we analyze a model based on evolutionary game theory that captures this feedback in the context of vaccine scares, and that also includes social learning. Vaccine risk perception evolves over time according to an exogenously imposed curve. We test the model against vaccine coverage data and disease incidence data from two vaccine scares in England & Wales: the whole cell pertussis vaccine scare and the MMR vaccine scare. The model fits vaccine coverage data from both vaccine scares relatively well. Moreover, the model can explain the vaccine coverage data more parsimoniously than most competing models without social learning and/or feedback (hence, adding social learning and feedback to a vaccine scare model improves model fit with little or no parsimony penalty). Under some circumstances, the model can predict future vaccine coverage and disease incidence--up to 10 years in advance in the case of pertussis--including specific qualitative features of the dynamics, such as future incidence peaks and undulations in vaccine coverage due to the population's response to changing disease incidence. Vaccine scares could become more common as eradication goals are approached for more vaccine-preventable diseases. Such models could help us predict how vaccine scares might unfold and assist mitigation efforts.

Figure 1. Whole cell pertussis vaccine coverage (solid line) and pertussis case notifications (dashed line), England & Wales 1971–1988 (a); measles-mumps-rubella vaccine coverage (solid line) and lab-confirmed measles case notifications (dashed line), England & Wales 1995–2009 (b).

Media reports of alleged vaccine risks began in 1974 for pertussis and 1998 for MMR , . Vaccine coverage is defined as percentage completing their primary courses by their second birthday. Hence, to correct for the ambiguity in precise age of vaccination in the model and allow comparison with case notification data, the vaccine coverage data in this figure are shifted by one year.

Figure 2. Parsimony analysis of behavioral model for the pertussis vaccine scare: vaccine coverage data (solid black line) and best-fitting model (dashed blue line) under behavioral model with both social learning and feedback (a, c, e, g, i) and reduced behavioral model with neither (b, d, f, h, j), under risk evolution curves #1–#5 (left-hand column).

Red lines are 50 bootstrapped samples. Numerical values in subpanels are AICc scores: lower values indicate greater parsimony.

Figure 3. Parsimony analysis of behavior-incidence model and the reduced model with neither social learning nor feedback under risk evolution curves #1–#5 (left-hand column), for the MMR vaccine scare: best fitting model (red) and vaccine coverage data (black).

The numerical value in the figure inset is the AICc score.

Figure 4. Predictive analysis of behavior-incidence model for the pertussis vaccine scare: predictions up until 1988 were made using data up until t _fit = 1975 (a, b); 1977 (c, d), 1978 (e, f) and 1988 (g, h) for both vaccine coverage (a, c, e, g) and case notifications (b, d, f, h).

Best fitting model (blue dots), 50 realizations from PSA (red lines), vaccine coverage and disease incidence data used to fit model (t≤t _fit; thick black lines), and data used to evaluate model predictions (t>t _fit; dashed black lines) are shown.

Figure 5. Predictive analysis of behavior-incidence model for the MMR vaccine scare: predictions up until 2009 were made using data up until t _fit = 2000 (a, b); 2004 (c, d), 2005 (e, f) and 2009 (g, h) for both vaccine coverage (a, c, e, g) and case notifications (b, d, f, h).

Best fitting model (blue dots), 50 realizations from PSA (red lines), vaccine coverage and disease incidence data used to fit model (t≤t _fit; thick black lines), and data used to evaluate model predictions (t>t _fit; dashed black lines) are shown.