Identifying postelimination trends for the introduction and transmissibility of measles in the United States

Abstract

The continued elimination of measles requires accurate assessment of its epidemiology and a critical evaluation of how its incidence is changing with time. National surveillance of measles in the United States between 2001 and 2011 provides data on the number of measles introductions and the size of the resulting transmission chains. These data allow inference of the effective reproduction number, Reff, and the probability of an outbreak occurring. Our estimate of 0.52 (95% confidence interval: 0.44, 0.60) for Reff is smaller than prior results. Our findings are relatively insensitive to the possibility that as few as 75% of cases were detected. Although we confirm that measles remains eliminated, we identify an increasing trend in the number of measles cases with time. We show that this trend is likely attributable to an increase in the number of disease introductions rather than a change in the transmissibility of measles. However, we find that transmissibility may increase substantially if vaccine coverage drops by as little as 1%. Our general approach of characterizing the case burden of measles is applicable to the epidemiologic assessment of other weakly transmitting or vaccine-controlled pathogens that are either at risk of emerging or on the brink of elimination.

Keywords: United States; disease elimination; effective reproduction number; heterogeneity of transmission; measles; preventable disease; transmissibility; vaccine coverage.

Figure 1.

Inference results for the transmission of measles in the United States during 2001–2011. A) The 95% confidence region for average chain size and the probability of an outbreak (defined as a chain having at least 3 cases) are shown for the negative binomial model under the assumption of perfect observation (black contour). These results were then modified for the scenario in which each case was observed with an independent probability of 75% (light gray contour). For each scenario, the maximum likelihood estimate is indicated by the bullet point. The dotted curve shows the relationship between average chain size and the probability of an outbreak when homogeneous transmission is assumed (i.e., the number of infections that are attributed to a randomly chosen case is Poisson distributed). The dashed curve, corresponding to k = 1, represents transmission with an intermediate degree of heterogeneity (i.e., the number of infections that are attributed to a randomly chosen case follow a geometric distribution). The dark gray line superimposed on the homogeneous transmission curve represents the truncated Poisson confidence interval of previously published analyses (9). The confidence interval for the truncated Poisson model is represented by a line because this model has only 1 parameter. The confidence regions for the models that are based on a negative binomial offspring distribution are shown as 2-dimensional contours because these models have 2 parameters. B) Chain size predictions based on 75% case observation rate (light gray) or the truncated Poisson model (dark gray) (9). The observed data and the 95% error bars for these observations (determined by bootstrapping) are shown in black.

Figure 2.

Projections for how a decrease in immunity would change the transmission of measles (dark and light gray contours). The other lines and contours are identical to those in Figure 1.

Figure 3.

Trends in the incidence, introduction, and transmission of measles cases in the United States, 1997–2011. A) Data on the number of measles cases are shown along with 95% error bars obtained with the assumption of a Poisson distribution for the number of cases in any 1 year. When the number of cases is modeled as varying linearly by year (i.e., Poisson regression), the dashed and solid gray lines show the best fit of the data for the years 1997–2011 and 2002–2011, respectively. The vertical dotted line indicates when measles was declared to be eliminated in the United States. B) The number of cases of measles depends on both the number of introductions of measles into the United States and on the transmissibility of measles (as represented by the effective reproduction number, R_eff). C) Postelimination data (from 2002–2011) on the number of introductions of measles cases are shown along with 95% error bars. A Poisson process for disease introduction is assumed. The gray line shows results for a linear regression of the data. D) The inferred values for the R_eff for each postelimination year (from 2002–2011) are plotted along with 95% confidence intervals and the best linear fit. The inference of R_eff is based on the assumption that the number of infections caused by each case follows a negative binomial distribution.