The recent increase in measles cases in California may raise questions regarding the continuing success of measles control. To determine whether the dynamics of measles is qualitatively different in comparison to previous years, we assess whether the 2014-2015 measles outbreak associated with an Anaheim theme park is consistent with subcriticality by calculating maximum-likelihood estimates for the effective reproduction number given this year’s outbreak, using the Galton-Watson branching process model. We find that the dynamics after the initial transmission event are consistent with prior transmission, but does not exclude the possibility that the effective reproduction number has increased.

A recent outbreak of measles linked with one or more Disney theme parks has reinvigorated discussion of measles vaccination.^{,}^{,}^{,}

Between 2001 and 2011, the average number of individuals who became infected by one infectious case (the effective reproduction number, _{eff}_{eff}_{eff}

We used the Galton-Watson branching process model with our previously inferred dispersion parameter for measles, supplemented by sensitivity analysis. The number of new cases caused by each case is modeled by the negative binomial distribution, with parameters _{eff} and a dispersion parameter ^{,}

While heterogeneity and superspreading are key features of measles which must be taken into account, analysis of transmission at the very beginning of the epidemic—in the theme park—is subject to severe selection bias

Our analysis of the epidemic using the Galton-Watson process will assume a negative binomial distribution for the number of secondary cases caused by each active case. Assuming the negative binomial distribution ^{,}

These

The probability _{i }_{i}

Given _{i }_{i}.

We use values of the dispersion parameter _{eff}

To estimate an overall maximum likelihood effective reproduction number from an initial number of cases and a total cluster size, we use this assumed value of

The outbreak began with individuals exposed in Disneyland between December 17 and 20, 2014; 40 Californians were believed exposed during that period.

When 40 first-generation measles cases produce 91 additional linked secondary cases (for a total chain size of 131 including a putative single index case),

We conducted an additional sensitivity analysis in which we no longer assumed that the effective reproduction number was constant. Assuming that the approximately 48 cases reported in the two weeks immediately following the last of the 40 Disney-exposed cases to be the next generation of transmission outside Disneyland, we find maximum likelihood estimates of the effective reproduction number to be 1.20 (=48/40) (95% CI: 0.65, 2.45, assuming

Finally, if we assume 60 introductions per year into the US, and use the estimated effective reproduction number 0.52 and dispersion parameter 0.27 from the 2001-2011 data_{eff}

Probability of at least 131 cases (the chain size restricted to California) following 20, 40, or 60 first generation cases in California as a function of reproduction number _{eff}, with _{eff} and 95% CI based on data for measles transmission in the United States from 2001–2011.

Except for the substantial initial transmission event that occurred within the Disney theme parks, the transmission of measles seen in the recent outbreak is relatively consistent with data from the past decade. In particular, amplification from 40 cases to 91 additional cases is consistent with subcritical transmission, with each case failing, on average, to replace itself, but playing out over several generations of transmission. Our primary estimate of the reproduction number, 0.69, is higher than the number obtained from US national data for 2001-2011 (0.52), but the difference is not statistically significant. Our second estimate (in which we allowed the effective reproduction number

Use of the Galton-Watson process with a negative binomial distribution accounts for heterogeneity in transmission, but we are limited in that our estimated dispersion parameter (

Our primary analysis also assumed a constant value for the reproduction number during the entire outbreak. However, the onset of rash of the first case was on Dec. 28, 2014, while the outbreak proper did not come to the attention of the public until Jan. 6

It is important to note that the epidemiology of recent years post-elimination illustrates that even with the absence of endemic measles, transmission can still occur with imported infections and susceptible individuals.

All authors have confirmed that they have no financial, personal or professional competing interests to report.

We gratefully acknowledge useful discussions with J. Zipprich and K. Harriman at the California Department of Public Health.

Check out the PLOS Science Wednesdays AMA (Ask Me Anything) series from June 3rd, 2015 featuring Seth Blumberg and Jennifer Zipprich on the topic of vaccination and measles transmission: http://plos.io/measlesama7