Influenza recurs seasonally in temperate regions of the world; however, our ability to predict the timing, duration, and magnitude of local seasonal outbreaks of influenza remains limited. Here we develop a framework for initializing real-time forecasts of seasonal influenza outbreaks, using a data assimilation technique commonly applied in numerical weather prediction. The availability of realtime, web-based estimates of local influenza infection rates makes this type of quantitative forecasting possible. Retrospective ensemble forecasts are generated on a weekly basis following assimilation of these web-based estimates for the 2003-2008 influenza seasons in New York City. The findings indicate that real-time skillful predictions of peak timing can be made more than 7 wk in advance of the actual peak. In addition, confidence in those predictions can be inferred from the spread of the forecast ensemble. This work represents an initial step in the development of a statistically rigorous system for real-time forecast of seasonal influenza. Kalman filter | absolute humidity W orldwide, influenza produces 3-5 million severe illnesses annually and kills an estimated 250,000-500,000 people (1). In temperate regions, influenza characteristically recurs during winter when absolute humidity levels are low (2, 3), but at present our ability to predict important details of these seasonal influenza outbreaks is limited. Indeed, much public health benefit could be gleaned from early, skillful prediction of the onset, peak, duration, and magnitude of local influenza outbreaks. Mathematical models of infectious disease transmission have been in use for over a century (4). These models have been developed to study the dynamic properties of disease transmission (5-7), determine the biological characteristics of specific pathogens (8, 9) , and analyze historical transmission behavior during documented outbreak events (10). More recently, infectious disease model simulations have been performed retrospectively in conjunction with statistical filtering methods to provide maximum-likelihood parameter estimation (11, 12) and improved epidemic simulation through time and physical space (13-16). Filtering techniques iteratively update, or adjust, model simulation estimates of the dynamic state, e.g., population infection rates, using real-world observations of that state, as the model is integrated through time. Because the state is only intermittently, or partially, observed-i.e., infections may be observed only for some locations and times, and some state variables, such as population susceptibility rates, may not be observed at all-and because these partial observations themselves contain error, the filter endeavors to balance the relative information contained in the observations and the model simulation. At the same time, the filtering process can also be used to estimate epidemiologically significant parameters within a model. These same filtering techniques, by constraining the model state and parameters, can potentially be used to enhance the ability of a model to skillfully forecast disease transmission. Heretofore, such attempts at prediction have been applied in a very limited fashion without thorough evaluation of the skill, or uncertainty, of the forecast (17-19). In theory, infectious disease predictions could be developed, validated, and produced in a fashion similar to that of the forecasts generated for numerical weather prediction (NWP) (20). Much like weather dynamics, infectious disease dynamics are nonlinear and intrinsically chaotic. These characteristics make the evolution of these purely deterministic systems highly sensitive to their current conditions, such that very small differences in the current state can rapidly amplify through time to divergent future outcomes (21, 22) . Similarly, for mathematical models representing these nonlinear systems, errors in the estimate of the initial dynamic state of the system grow as these models are integrated into the future. This error growth degrades the accuracy of a forecast the farther into the future it is extended and imposes a formal limit on predictability (23). Such initial error growth is additionally exacerbated by the use of imperfect, simplified model representations of the true system. Together, the nonlinearity of the modeled system and the shortcomings of the model representation lead to a degradation of prediction quality the farther forward in time one forecasts. To counter this error growth, NWP uses data assimilation techniques, such as filtering, to repeatedly reinitialize dynamic weather models, using the latest available observations and knowledge of the error associated with those observations. In NWP this reinitialization or assimilation is performed frequently (e.g., every 6 h) and the newly initialized model is then integrated forward in time (e.g., 7 d) to create a new set of weather forecasts. Metrics for evaluating the real-time skill of these model-data assimilation system forecasts have been developed to validate these predictions. To realize such a model-data assimilation prediction system for infectious disease, real-time or near real-time observations of population-level disease status must be available. For influenza, near real-time online-search query estimates of influenza infection rates have recently been developed and validated historically against US Centers for Disease Control and Prevention (CDC) official estimates of influenza-like illness (ILI) (24). At the time of this writing, these Google Flu Trends (GFT) data were available for 28 countries, as well as by district, province, state, or municipality within these countries. These near real-time population-level data make application of model-data assimilation prediction practicable. Here we apply a data assimilation method called the ensemble adjustment Kalman filter (EAKF) (20) to entrain weekly GFT estimates of ILI (24, 25) into a simple humidity-forced susceptibleinfectious-recovered-susceptible (SIRS) mathematical model of influenza (3). The EAKF is a recursive filtering technique that combines observations with a temporally evolving ensemble of model simulations to generate a posterior estimate of the model state (20). This process nudges the ensemble mean toward the observations and simultaneously contracts the ensemble variance, thus constraining the model state and parameters. Before using the GFT estimates we first validated the functionality of the combined SIRS-EAKF framework, using a synthetic,
It also shows the current ILI counts in the US in a map format REF .
Forecasting seasonal outbreaks of influenza
Proceedings of the National Academy of Sciences of the United States of America
Proceedings of the National Academy of Sciences of the United States of America
Geography Medicine