Approximate Bayesian algorithm to estimate the basic reproduction number in an influenza pandemic using arrival times of imported cases

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 simulation 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 o 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.