Predictive Science Influenza Modeling

Influenza-Like-Illness (ILI) Forecast: %ILI is measured by the CDC as the percent of outpatient visits with ILI symptoms. The shaded (grey) portion of the figure is the modeled %ILI 1-4 weeks forecast with distribution quantile ranges illustrated by red (1-99%), yellow (5-95%), and green (25-75%). See the 'About' tab for more information.

Distributions for annual forecast targets. Probability distributions describing model solutions/forecast for onset week (as defined by CDC), peak week, and peak intensity. Where an actual value is detected in the data, it is represented as a grey line. The shaded area indicates a sliding window of 'correct' predictions as defined by the CDC Flu Challenge guidelines.


In the infectious disease group here at Predictive Science, we run simulations to predict influenza proliferation on a week-to-week basis in the United States. The 'gold standard' for measuring the spread of flu is the Percent Influenza-Like-Illness (%ILI) data collected and distributed by the Centers for Disease Control (CDC). Thus our model seeks to forecast %ILI values for future weeks.


We use an Suseptible-Infectious-Recovered (SIR) model with a time-dependent reproduction number R0(t). Reproduction number can be understood as a measure of infectiousness. In our models R0(t) is a function of school schedule and/or specific humidity.


Fitting the model to the data is done via Markov Chain Monte Carlo (MCMC) process. This procedure maps the probability distribution, revealing not only the best fit, but also likely model variations.

CDC Flu Forecasting Competition

Although not demonstrated here, we also mix historical averages and linear predictions into our forecasts for the CDC Flu Challenge. These additions are especially helpful in weeks where %ILI is driven by non-flu diseases.

Each year, the CDC uses historic influenza data to calculate a %ILI 'onset value' for each region (grey dashed line in plot). Flu season onset is then defined as the first instance where %ILI is above the onset value for three consecutive weeks. 'Onset week' is the first of these three weeks.

User Selections

Epidemic Week: Week of the year as defined by the Morbidity and Mortality Weekly Report (MMWR). In this setting 'epidemic week' selects the portion of the flu season to fit the model to.

View all models The default setting 'Forecasts' shows the final forecast submitted for each region/week combination. These forecasts are based primarily on the best mechanistic model-fit, but also include aspects from historic statistics and recent-week trends. For the 1-4 week forecasts, color shading indicates the following quantiles: green - 25% to 75%, yellow - %5 to 95%, green - %1 to %99. The second option 'All Models' accesses the results of all the MCMC-fit SIR models.


%ILI: The percent of outpatient visits for influenza-like-illness at participating clinics. ILI is a diagnosis made by physicians when the patient has a fever as well as a sore throat and/or cough without a known cause other than influenza.

school: Proportion of student-days on break for a given week. A value of 1 indicates that all schools are on break for all five weekdays for the given week. A value of 0 indicates that all schools are in session for the entire week. Intermediate values describe the cases where some (but not all) schools are on break or students have partial weeks off.

SH: Specific humidity (kg/kg) from NASA NLDAS-2 data. Points up to 'Epidemic Week' are observed values. Points after 'Epidemic Week' are historic averages.