The impact of past vaccination coverage and immunity on pertussis resurgence

Abstract

The resurgence of pertussis over the past decades has resulted in incidence levels not witnessed in the United States since the 1950s. The underlying causes have been the subject of much speculation, with particular attention paid to the shortcomings of the latest generation of vaccines. We formulated transmission models comprising competing hypotheses regarding vaccine failure and challenged them to explain 16 years of highly resolved incidence data from Massachusetts, United States. Our results suggest that the resurgence of pertussis is a predictable consequence of incomplete historical coverage with an imperfect vaccine that confers slowly waning immunity. We found evidence that the vaccine itself is effective at reducing overall transmission, yet that routine vaccination alone would be insufficient for elimination of the disease. Our results indicated that the core transmission group is schoolchildren. Therefore, efforts aimed at curtailing transmission in the population at large, and especially in vulnerable infants, are more likely to succeed if targeted at schoolchildren, rather than adults.

Figure 1. Pertussis incidence data in Massachusetts, United States, 1990–2005

The figure displays temporal trends of age-specific pertussis incidence data. (A) Monthly case reports by age group. (B) Annual case reports (per 100,000) by age group. The black line represents the overall incidence. (C) Case fraction among age groups. (D) Cumulative case fraction among age groups. For each age group on the x-axis, the corresponding value on the y-axis represents the fraction of cases of lower or equal age. Each line represents a distinct calendar year.

Figure 2. Testing of transmission model

The figure shows several analyses of the model fit to the observed incidence data. (A) Annual case reports (thick lines), 5 stochastic realizations (thin lines), and prediction range (grey area) from 1,000 stochastic realizations of the model. These are not one-step ahead predictions; simulations were started in 1990, with initial conditions fixed by conditioning on the first data point (see Materials and Methods/Model assessment). The y-axis differs between panels for visual clarity. (B) Quantitative comparison of the agreement between model and data based on one-month-ahead predictions. Each point is colored according to the age group. The observed monthly cases (x-axis) and the simulated monthly cases (y-axis), were calculated by averaging across 5,000 stochastic realizations. The dashed grey line has slope 1 and intercept 0, corresponding to a perfect fit. The overestimation at low case numbers is due to the fact that predictions are not single realizations, but expectations of non-negative random variables and, as such, are bounded away from 0 (see fig. S11 for the comparable figure on simulated data). The corresponding generalized R²—measuring the proportion of variance explained by the model to that not explained by age alone—is 0.35. (C) Predictability as a function of the generation time. For each generation time, the figure shows the distribution of R² for 100 synthetic data sets, generated assuming the true model is known (see fig. S10). The dashed grey line indicates the R² obtained by comparison with the real data. (D) Quantitative comparison of the agreement between model and data based on six-month-ahead predictions started annually in August (R² = 0.40; see figs. S12–S13 for values of R² calculated at other forecast horizons and other base months). For visual clarity, the y-axis does not start at 0 in panels A and C.

Figure 3. Dissecting pertussis epidemiology in Massachusetts

Model hindcasts during 1990–2005 [panels (A)–(D)]. The panels represent the filtering means (that is, the average predicted values at each time conditioned on all the data up to that time) for several state variables: naïve infections (A), post-vaccine infections (B), fraction susceptible to a post-vaccine infection (C), and fraction recovered (D). Panels A and B represent total predicted infections, before applying the reporting model. (E) Model hindcasts before 1990. Five stochastic realizations of the total incidence (naïve plus post-vaccine infections) are presented. The dotted line at year 1940 indicates the start date of mass vaccination assumed in the model. In the absence of immunization data before 1970, we assume that the vaccine coverage had ramped up between 1940 and 1955 (see model formulation in the Materials and Methods). For visual clarity, the y-axis does not start at 0. (F) Comparison of model predictions with empirical studies that quantified DTaP vaccine failure by estimating relative changes (over age) in the odds of acquiring pertussis. We simulated the waning model (with identical wP- and DTaP-derived immunity) during 2006–2015 and used log-linear regression to calculate the yearly relative change (over age) in the odds of acquiring pertussis in children aged 5–10 years, i.e., 0–5 years after receipt of the fifth vaccine dose (see model predictions in the DTaP era in the Materials and Methods). The distribution is based on 10⁴ simulations, accounting for parametric uncertainty by sampling from the bootstrap distribution. Also presented are estimates from 3 empirical studies in the US [Klein et al. (46), Misegades et al. (48), and Tartof et al. (49))] and from a meta-analysis [McGirr et al. (47)].

Figure 4. Predicted impact of single-booster vaccination

Simulations of the waning model were run until the end of 2005, at which point a 25% fraction of susceptible individuals in a target age group (5–10, 10–20, 20–40, or ≥40 years old) was moved to the vaccinated class. The model was run for the subsequent 10 years (2006–2015) and the age-specific total annual infections (i.e., naïve and post-vaccine infections, calculated before applying the observation model) were compared to a control scenario without booster vaccination. Each boxplot is based on 10⁴ stochastic simulations, accounting for parametric uncertainty of the waning model by sampling parameters from the bootstrap distribution. For each intervention, the number indicates the relative difference between the median simulated incidence and that of the control scenario. The figure shows the predicted impact in unvaccinated infants aged 0–4 months, the age group most at risk of severe disease (see fig. S14 for the corresponding figure in every age group). For visual clarity, the y-axis does not start at 0.