Table 2 Major modeling approaches used to generate influenza outbreak forecasts*

Agent-based models

These are computational systems in which persons are treated as individual agents that can interact with other agents and their environment based on specific rules.

These models have been used to address questions relating to the impact of control measures and changes in individual behavior during an outbreak. They allow for interactions between individuals and between individuals and their environments, and can therefore enable the forecasting of influenza dynamics under different intervention and resource allocation scenarios.

One difficulty in applying these models is the assumptions under which they operate, compounded by our limitations in understanding human behavior and contact networks. They are also computationally challenging and often require supercomputers.

Compartmental models

These models divide the population into compartments based on disease states and define rates at which individuals move between compartments. Examples include susceptible–infectious–recovered (SIR) and susceptible–exposed–infectious–recovered (SEIR) models.

Compartmental models are attractive due to their simplicity and well-studied behavior. These models are typically extended by defining multiple compartments to introduce subpopulations, or used in combination with other approaches, such as particle filtering, for influenza forecasting [20, 21].

The usual fully mixed, homogenous population assumption fails to capture the differences in contact patterns for different age groups and environments.

Ensemble models

Ensemble modeling is the process of running two or more models and synthesizing the results into a single forecast with the intent of improving the accuracy. The individual models may be nearly identical to each other or may differ greatly.

Ensemble models typically predict future observations better than a single model. Individual models in the ensemble can be weighted using recent or historical performance, or using a more complex algorithm.

The choice of which forecasts to include and how to weight the individual forecasts in the final ensemble may vary and is not standardized for infectious disease forecasting.

Metapopulation models

In between agent-based and compartmental models, populations are represented in structured and separated discrete patches and subpopulations interact through movement. Epidemic dynamics can be described within patches using clearly defined disease states such as in compartmental models.

The detailed mobility networks used in some of these models can enable reliable description of the diffusion pattern of an ongoing epidemic. These models have also been used to evaluate the effectiveness of various measures for controlling influenza epidemics.

Similar to agent-based models, empirical measurement or assumptions concerning interactions and movement is challenging.

Method of analogs

The method of analogs is a nonparametric forecasting approach. Forecasting is based on matching current influenza patterns to patterns of historical outbreaks.

The onset of seasonal influenza epidemics varies from year to year in most countries in the Northern hemisphere. As the method of analogs is nonparametric, it does not require explicit assumptions about underlying distributions or seasonality.

These forecasts rely on historical data which are often limited or not available. Limitations include the difficulty in finding similar patterns from historical outbreaks.

Time series models

These models typically use the Box-Jenkins approach and assume that future values can be predicted based on past observations.

Can capture lagged relationships that usually exist in periodically collected data. In addition, temporal dependence can also be represented in models that are capable of capturing trend and periodic changes.

Influenza activity is not consistent from season to season, which could impose limitations to these methods.