International travelers and genomics uncover a ‘hidden’ Zika outbreak

Nathan D. Grubaugh; Sharada Saraf; Karthik Gangavarapu; Alexander Watts; Amanda L. Tan; Rachel J. Oidtman; Jason T. Ladner; Glenn Oliveira; Nathaniel L. Matteson; Moritz U.G. Kraemer; Chantal B.F. Vogels; Aaron Hentoff; Deepit Bhatia; Danielle Stanek; Blake Scott; Vanessa Landis; Ian Stryker; Marshall R. Cone; Edgar W. Kopp; Andrew C. Cannons; Lea Heberlein-Larson; Stephen White; Leah D. Gillis; Michael J. Ricciardi; Jaclyn Kwal; Paola K. Lichtenberger; Diogo M. Magnani; David I. Watkins; Gustavo Palacios; Davidson H. Hamer; Lauren M. Gardner; T. Alex Perkins; Guy Baele; Kamran Khan; Andrea Morrison; Sharon Isern; Scott F. Michael; Kristian G. Andersen

We used two data types-locally acquired cases by country and Florida travel cases by country-to inform estimates of per capita local incidence in Cuba on a scale comparable to local incidence in other countries. We limited our analysis of countries besides Cuba to those with a correlation between monthly local and travel cases >0.25 (n=27), which appeared to be a natural breakpoint in the distribution of correlations. For each, we used the fda (https://cran.r-project.org/web/packages/fda/index.html) package in R to model per capita local incidence of Zika over time with univariate cubic B-spline functions with four knots per year for two years (2016-2017) described by parameters Ꭿ. We assumed that incidence among travelers from each country followed the same temporal pattern as local incidence but the two differed in magnitude by a factor Ꮃ, which could be due to differences in exposure or health-seeking behavior between international travelers and the general population. To estimate Ꭿ and Ꮃ for each of the 27 countries, we modeled local and travel incidence for each month as independent binomial random variables, with incidence as the number of "successes" and country population and number of travelers, respectively, as the number of "trials." Logit-transformed values of the spline functions informed the probability of success in each trial. Based on this likelihood formulation and with non-informative priors, we estimated Ꭿ and Ꮃ for each country using a Metropolis-Hastings implementation of Markov chain Monte Carlo (MCMC). We assessed convergence by calculating Gelman-Rubin statistics on five replicate chains, and we performed posterior predictive checks on cumulative local incidence (Fig. S2 ) and travel incidence (Fig. S3 ) (Thompson Hobbs and Hooten, 2015) . On the basis of Bayesian p-values < 0.05 on these posterior predictive checks, we removed four countries from subsequent analyses (leaving n=23 countries). To estimate per capita local incidence in Cuba, we first estimated Ꭿ for Cuba in a similar manner, but based on travel data only. We then took 10 4 values of Ꮃ drawn randomly from the posteriors of Ꮃ pooled across 23 countries and multiplied them by random samples from the posterior of per capita travel incidence curves from Cuba to obtain a set of 10 4 predictions of per capita local incidence curves for Cuba. R code and posterior samples are available at: https://github.com/andersen-lab/paper_2018_cuba-travelzika.