With an estimated $10.4 billion in medical costs and 31.4 million outpatient visits each year, influenza poses a serious burden of disease in the United States. To provide insights and advance warning into the spread of influenza, the U.S. Centers for Disease Control and Prevention (CDC) runs a challenge for forecasting weighted influenza-like illness (wILI) at the national and regional level. Many models produce independent forecasts for each geographical unit, ignoring the constraint that the national wILI is a weighted sum of regional wILI, where the weights correspond to the population size of the region. We propose a novel algorithm that transforms a set of independent forecast distributions to obey this constraint, which we refer to as probabilistically coherent. Enforcing probabilistic coherence led to an increase in forecast skill for 79% of the models we tested over multiple flu seasons, highlighting the importance of respecting the forecasting system's geographical hierarchy.

Effective disease monitoring provides a foundation for effective public health systems. This has historically been accomplished with patient contact and bureaucratic aggregation, which tends to be slow and expensive. Recent internet-based approaches promise to be real-time and cheap, with few parameters. However, the question of when and how these approaches work remains open. We addressed this question using Wikipedia access logs and category links. Our experiments, replicable and extensible using our open source code and data, test the effect of semantic article filtering, amount of training data, forecast horizon, and model staleness by comparing across 6 diseases and 4 countries using thousands of individual models. We found that our minimal-configuration, language-agnostic article selection process based on semantic relatedness is effective for improving predictions, and that our approach is relatively insensitive to the amount and age of training data. We also found, in contrast to prior work, very little forecasting value, and we argue that this is consistent with theoretical considerations about the nature of forecasting. These mixed results lead us to propose that the currently observational field of internet-based disease surveillance must pivot to include theoretical models of information flow as well as controlled experiments based on simulations of disease.