Contents lists available at ScienceDirect Travel Medicine and Infectious Disease journal homepage: www.elsevier.com/locate/tmaid Approximate Bayesian algorithm to estimate the basic reproduction number in an influenza pandemic using arrival times of imported cases Ka Chun Chong a,b , Benny Chung Ying Zee a,b , Maggie Haitian Wang a,b,* a Division of Biostatistics, JC School of Public Health and Primary Care, The Chinese University of Hong Kong, Hong Kong, China b Clinical Trials and Biostatistics Laboratory, Shenzhen Research Institute, The Chinese University of Hong Kong, Hong Kong, China ARTICLE INFO Keywords: Basic reproduction number Epidemic models Travel data SIR model Influenza pandemic Surveillance ABSTRACT Background: In an influenza pandemic, arrival times of cases are a proxy of the epidemic size and disease transmissibility. Because of intense surveillance of travelers from infected countries, detection is more rapid and complete than on local surveillance. Travel information can provide a more reliable estimation of transmission parameters. Method: We developed an Approximate Bayesian Computation algorithm to estimate the basic reproduction number (R 0 ) in addition to the reporting rate and unobserved epidemic start time, utilizing travel, and routine surveillance data in an influenza pandemic. A simulation was conducted to assess the sampling uncertainty. The estimation approach was further applied to the 2009 influenza A/H1N1 pandemic in Mexico as a case study. Results: In the simulations, we showed that the estimation approach was valid and reliable in different simu- lation settings. We also found estimates of R 0 and the reporting rate to be 1.37 (95% Credible Interval [CI]: 1.26–1.42) and 4.9% (95% CI: 0.1%–18%), respectively, in the 2009 influenza pandemic in Mexico, which were robust to variations in the fixed parameters. The estimated R 0 was consistent with that in the literature. Conclusions: This method is useful for officials to obtain reliable estimates of disease transmissibility for strategic planning. We suggest that improvements to the flow of reporting for confirmed cases among patients arriving at different countries are required. 1. Introduction Basic reproduction number (R 0 ) is an epidemiological metric to measure the number of secondary infections generated on average by an infected patient in a whole susceptible population. It is useful in summarizing the transmissibility of an infectious disease in a popula- tion. If R 0 > 1, an infection will persist in a population and become endemic because each infected person is expected to have more than one transmission. In contrast, if R 0 < 1, the disease transmission cannot be sustained. An underestimation of R 0 could lead to un- preparedness among officials on disease mitigation. The estimated R 0 can be fitted through feeding syndromic, ser- ological data and laboratory-confirmed counts into simple statistical models (e.g., exponential growth curve) or traditional Susceptible- Infectious-Recovered (SIR) models [1–4]. Nevertheless, common esti- mation approaches using such data required an assumption of no un- derreporting, although several approaches were developed to adjust for this problem [5]. Recently, syndromic data were commonly used for influenza prediction and R 0 estimation. For example, Ginsberg et al. demonstrated that Google search queries could track weekly influenza activity [6]. Conversely, serological data could be used to infer influ- enza transmissibility, although in this case, the time for diagnostic confirmation is longer [7,8]. Compared with other kinds of data, ser- ological data could be used to infer asymptomatic infections without being affected by under-reporting. To overcome the underreporting problem in R 0 estimation using surveillance data, travel data from the exported cases can provide ad- ditional information. The arrival times of infected cases from the ori- ginating country are a metric of the expansion of the epidemic and the interaction thereof with international transportation networks [9–11]. In addition to using routine surveillance data, the arrival times of ex- ported cases could help reduce the errors incurred by undetected local cases. Compared with serological data, this information is usually more readily accessible. In this study, we developed an approach to estimate R 0 and the reporting rate for a new influenza pandemic using an Approximate Bayesian Computation (ABC). The ABC algorithm adopted the use of routine surveillance data as well as information on exported cases, i.e., https://doi.org/10.1016/j.tmaid.2018.04.004 Received 27 July 2015; Received in revised form 6 April 2018; Accepted 9 April 2018 * Corresponding author. Division of Biostatistics, JC School of Public Health and Primary Care, The Chinese University of Hong Kong, Hong Kong, China. E-mail addresses: marc@cuhk.edu.hk (K.C. Chong), bzee@cuhk.edu.hk (B.C.Y. Zee), maggiew@cuhk.edu.hk (M.H. Wang). Travel Medicine and Infectious Disease xxx (xxxx) xxx–xxx 1477-8939/ © 2018 Elsevier Ltd. All rights reserved. Please cite this article as: Chong, K.C., Travel Medicine and Infectious Disease (2018), https://doi.org/10.1016/j.tmaid.2018.04.004