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.
Highlights
Vaccine coverage in England & Wales during the whole cell pertussis vaccine scare in the 1970s and the measles-mumpsrubella (MMR) vaccine scare in the 1990s share a common pattern of decline and recovery over many years (Figure 1)
Theory suggests that vaccine scares exemplify a ‘‘free-rider problem’’: vaccine-generated herd immunity can reduce disease incidence to such low levels that vaccine risks appear large in comparison, causing some individuals to cease vaccinating
We explored five possible shapes for v(t): N Curve #1: instantaneous increase in perceived vaccine risk followed by linear decline: set Dincrease = Dmax = 0 and fit vpre, s, Ddecrease; N Curve #2: instantaneous increase followed by plateau followed by instantaneous decline: set Dincrease = Ddecrease = 0 and fit vpre, s, Dmax; N Curve #3: instantaneous increase followed by plateau followed by linear decline: set Dincrease = 0 and fit vpre, s, Ddecrease, Dmax; N Curve #4: linear increase followed by plateau followed by instantaneous decline: set Ddecrease = 0 and fit vpre, s, Dincrease, Dmax; N Curve #5: linear increase followed by plateau followed by linear decline: fit vpre, s, Ddecrease, Dincrease, Dmax
Summary
Vaccine coverage in England & Wales during the whole cell pertussis vaccine scare in the 1970s and the measles-mumpsrubella (MMR) vaccine scare in the 1990s share a common pattern of decline and recovery over many years (Figure 1). MMR coverage declined much less and the resulting outbreaks were smaller, measles was declared endemic again by 2008 [1]. Theory suggests that vaccine scares exemplify a ‘‘free-rider problem’’: vaccine-generated herd immunity can reduce disease incidence to such low levels that vaccine risks appear large in comparison, causing some individuals to cease vaccinating. These non-vaccinators effectively ‘‘free ride’’ on the herd immunity generated by vaccinators. A growing literature combines mathematical models of disease transmission with game theory or other behavioral models to explore the feedback loop that connects disease incidence and vaccinating behavior among individuals: disease incidence influences vaccinating behavior through individuals wanting to avoid health risks, and vaccinating behavior in turn influences disease incidence through herd immunity generated by vaccination [2,3,4,5,6,7,8,9,10,11,12,13,14]
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