Dangers of vaccine refusal near the herd immunity threshold: a modelling study Nina H Fefferman, Elena N Naumova

Summary Background Childhood vaccination remains the focus of heated public debate. Parents struggle to understand the potential risks associated with vaccination but both parents and physicians assume that they understand the risks associated with infection. This study was done to characterise how modern vaccination practices have altered patient risks from infection. Methods In this modelling study, we use mathematical analysis to explore how modern-era vaccination practices have changed the risks of severe outcomes for some infections by changing the landscape for disease transmission. We show these effects using published data from outbreaks in the USA for measles, chickenpox, and rubella. Calculation of risk estimation was the main outcome of this study. Findings Our calculations show that negative outcomes are 4·5 times worse for measles, 2·2 times worse for chickenpox, and 5·8 times worse for rubella than would be expected in a pre-vaccine era in which the average age at infection would have been lower. Interpretation As vaccination makes preventable illness rarer, for some diseases, it also increases the expected severity of each case. Because estimates of case risks rely on data for severity generated during a pre-vaccine era they underestimate negative outcomes in the modern post-vaccine epidemiological landscape. Physicians and parents should understand when making decisions about their children’s health and safety that remaining unvaccinated in a predominantly vaccine-protected community exposes their children to the most severe possible outcomes for many preventable diseases. Funding None.

Introduction In the USA, parental decisions to refuse available vaccines for their children have been increasing during the past decades.1,2 Media attention of parents voicing concerns about vaccine safety, religious teachings, or simple resistance to government-mandated health practices has brought these issues into the centre of national and international debate.3–5 Outbreaks of diseases for which we have adequate available vaccines, such as measles, mumps, and rubella, still occur, and studies6,7 have confirmed that areas with high rates of vaccine refusal are at an increased risk of outbreaks (at 2–22 times higher risk of disease outbreak, depending on the disease). As more of the population are vaccinated, the vaccination of each additional person provides a diminishing protective return because of the reduced number of potential carriers of infection circulating in the population.8 The individual incentive is to avoid vaccination while the rest of the population accepts the vaccine, thereby gaining indirect protection from immune individuals who are incapable of catching or carrying infection, making contact with an infected person from whom to catch the disease highly unlikely (ie, herd immunity9). This strategy provides some protection to those who are unvaccinated without incurring any of the potential risks or costs of the vaccine.

Analyses10 have shown how this notion leads to a conflict between personal interest and public health endeavours, and the most common argument against vaccine refusal (beyond that of ensuring informed consent) has therefore been one of compromise for the common good. However, surveys have confirmed that parents are naturally reluctant to vaccinate their own children simply to provide indirect protection to others.11 Although the individual risk of infection is diminished as more of the general population is protected, as fewer individuals catch the disease, an increase in the average age at first infection occurs.12 This increase in age at first infection is due to the relative frequency of contact between active infections and susceptible individuals decreasing as the susceptible pool is diluted by vaccine protection. For example, the average age of rubella infection in urban areas of Brazil shifted from 10–19 years to 15–29 years after the introduction of vaccination, even though the total number of cases was substantially decreased.13 For diseases in which severity of adverse health outcomes increases with age at time of infection, the risk of being one of the last people to be vaccinated can be high because as fewer people are infected, the age of infection will rise, making those who are infected last the worst affected. Although this pattern of increased risk with increased age is not the case with all infections, some of the vaccine-preventable diseases follow this Published online May 15, 2015

Lancet Infect Dis 2015 Published Online May 15, 2015 S1473-3099(15)00053-5 See Online/Comment S1473-3099(15)00054-7 Department of Ecology, Evolution, and Natural Resources, Rutgers University, New Brunswick, NJ, USA (Prof N H Fefferman PhD); Center for Discrete Mathematics and Theoretical Computer Science (DIMACS), Rutgers University, Piscataway, NJ, USA (Prof N H Fefferman, Prof E N Naumova PhD); and Tufts University Initiative for the Forecasting and Modeling of Infectious Diseases (Prof N H Fefferman, Prof E N Naumova), and Department of Civil and Environmental Engineering (Prof E N Naumova), Tufts University, Medford, MA, USA Correspondence to: Prof Nina H Fefferman, Department of Ecology, Evolution, and Natural Resources, Rutgers University, New Brunswick, NJ 08901, USA feff[email protected]



Research in context Evidence before this study This work is based on mathematical models and insights gleaned from application of those models to data from isolated outbreaks as examples of the concepts presented. As such, we do not mean that the data used should be taken as exhaustive; however, publications reporting epidemiological data from outbreaks of vaccine preventable diseases in developed countries were identified by searching PubMed and Google Scholar using the search terms “age”, “outcome”, “epidemiology”, and “MMR” to identify and select the first paper(s) in English that presented sufficient detail in the measurements to allow the desired analysis of all diseases.

of our knowledge, no previous effort has analysed these data to discover how vaccination practices in high-income countries change risks from infection for those that remain unprotected. We provide this first examination to show and describe how herd immunity and public protection increase the risks faced by unvaccinated individuals. Implications of all the available evidence Conversations physicians have with parents, caregivers, and patients about vaccination decisions should include discussion of modern risks of disease outcomes rather than only the risks associated with adverse reactions to vaccines versus the probability of contracting the disease.

Added value of this study Although all the conceptual elements in this study have already been discussed in the scientific literature, to the best

pattern.14–16 Such changes in disease dynamics at vaccination levels close to the threshold are a well recognised challenge in modelling of vaccine-preventable diseases.17 However, estimations of risk in public debates and in parental discussions with paediatricians do not incorporate the understanding that those who refuse vaccines at or near the threshold, thereby allowing for the reduction of community-level immunity to the point where herd immunity is no longer protective, risk having the worst health outcomes. Empirical evidence comparing pre-vaccine and postvaccine era outcomes shows a significant increase in mortality resulting from infection (eg, a 15 times higher prevalence of varicella infection before vaccination18). This directly counters the argument that everybody’s grandparents survived these diseases naturally, which is especially problematic because those who died during childhood in an earlier era did not father descendants. Rather than a diminishing benefit associated with vaccination, as the disease becomes rarer, for some diseases, an increasing benefit because of the heightened risk of more serious outcomes from infection might occur. However, the overall benefits from approaching herd immunity still outweigh the costs of increased adverse outcome risk from infection, but the tradeoff must be examined explicitly. In this study, we use mathematical analysis to explore how modern-era vaccination practices have changed the risks of severe outcomes for some infections by changing the landscape for disease transmission.

Methods Mathematical model of risk estimation To calculate the point at which the increase in risk of more severe illness would outweigh the decrease in risk of catching the disease achieved by approaching herd immunity threshold, we characterised severity of health 2

outcome from infection as a function (X) of age (a): X(a). We applied the well known association between the reproductive threshold (R0) and the average life expectancy (L), for average age of first infection (A): 19 ~L R0 = A

The effect of vaccine coverage can be expressed as follows: Reff = R0 (1 – v) Where v is the proportion of the population to be vaccinated; therefore, adequate immune coverage to generate herd immunity can be expressed as follows:12,19 v>1– 1 R0 Although these models have traditionally been applied to the general population, thus with v as a percentage of the total population, recent outbreaks20,21 have caused epidemiologists to re-assess this base population assumption.1,22 Outbreaks in areas with vaccine refusal rates that would, assuming the total base population, be theoretically insufficient to support continuing transmission have encouraged researchers to consider the possibility of increased contact occurring between unimmunised immigrants23 or families that reject vaccination,1 which artificially lowers the size of the base population appropriate for use in these calculations. The question then becomes simply, as v drops slightly below the threshold for adequate generation of herd immunity, how does the probability of an outbreak grow and how does the associated X(a) differ from the societal memory of severity of disease in a pre-vaccination era? Published online May 15, 2015


To show how increasing vaccination could yield increasing risks to those unvaccinated, we generate example X(a) curves from data in the published scientific literature by abstracting age-specific distributions of severe outcomes for measles (death rate per 100 000 people infected), chickenpox (hospital admission rate per 1000 people infected), and rubella (percentage of congenital rubella syndrome births), and fitted linear approximations to age ranges of interest (table 1, figure 1). All data was extracted from one study,14 the most recently available study that included sufficiently complete, relevant data to enable a calculated example. Current recommendations in the USA are to provide vaccine protection against measles and rubella (in the form of the measles, mumps, and rubella vaccination) and chickenpox (either in a joint measles, mumps, rubella, and varicella vaccine or in a single varicella vaccine) with the first dose at between 12 and 15 months of age, and the second dose at between 4 and 6 years of age.24 We make Midpoint of age (years)

Severity (diseasespecific)*


Risk rate


our calculations using the median of the range determined by the calculations mentioned for the estimated range.19 Public health practitioners would be well advised to recompute their own risk thresholds using local data for contact rates, vaccine efficacy, and life expectancy, rather than rely on the median. For full comparison, we further show the risks as vaccination coverage drops from near the herd immunity threshold to 0 (figure 2). To estimate the probability of outbreak occurrence based on vaccination rates falling below the level needed to produce herd immunity, we use estimations for measles in the UK,25 and assume that all unvaccinated people are at equal risk of infection once an outbreak is underway. Estimates for chickenpox and rubella were calculated assuming that the probability of outbreak occurrence scales proportionally with the unvaccinated reproductive number. Outbreaks for the unvaccinated populations are assumed to occur with a probability of 1; however, even without this assumption, the calculated risks would remain consistent across scenarios because this provides only a relative baseline risk. For use in real-world estimation, these probabilities would be most appropriately calculated locally because of their strong reliance on accurate local rates of exogenous reintroduction of exposure.






There was no funding source for this study. The corresponding author had full access to all the data in the study and had final responsibility for the decision to submit for publication.


Dangers of vaccine refusal near the herd immunity threshold: a modelling study.

Childhood vaccination remains the focus of heated public debate. Parents struggle to understand the potential risks associated with vaccination but bo...
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