Can a hierarchical model forecast seasonal epidemics across pathogens and regions?

One model, three pathogens, many states

The paper asks whether a single forecasting framework can handle several seasonal respiratory pathogens and many locations at once, instead of being rebuilt for each disease or region. The authors built INFLAenza, a Bayesian hierarchical spatiotemporal model, and tested it on weekly hospital admissions for COVID-19, influenza and RSV across US states. The target is short-term: forecasts one to four weeks ahead, the horizon public health agencies and hospitals use to prepare for surges.

The design rests on three features the authors observed in the data before modelling. All three diseases peak in winter, with an extra COVID-19 peak in late summer; individual seasons differ in severity from the average; and neighbouring states move together more than distant ones. For COVID-19, states sharing a border had a median correlation of 85% (95% CI: 82-86%), compared with 37% (95% CI: 25-43%) for states eight apart. The model is built to exploit exactly these regularities.

Seasonal shape plus short-term local deviation

INFLAenza treats each state's weekly admissions as a Poisson count scaled by that state's population, so the quantity being modelled is the per-person risk of hospitalisation in a given week. That risk is split into additive pieces: a national average, a state-specific intercept, a seasonal curve indexed by epidemiological week, and a short-term residual that captures everything the seasonal curve misses.

The seasonal curve is a smooth cyclic term that forces week 52 to connect back to week 1, so the model learns a repeating annual shape rather than fitting each week freely. The short-term residual has a part shared across all states and a part that lets a state's deviation depend on its neighbours, using a spatial model in which states sharing borders are more correlated than distant ones. Because the short-term term is autoregressive, its expected contribution shrinks toward zero as the forecast horizon lengthens, so longer forecasts revert toward the learned seasonal pattern while uncertainty around that pattern remains.

This decomposition is what makes the model portable. Nothing in it is specific to influenza or to a particular state; the disease-specific behaviour is learned from the training data rather than encoded by hand. The authors fit it with integrated nested Laplace approximations through the R-INLA package, and report that state and national forecasts are produced in minutes or less.

Roughly 40% better than a naive baseline

In retrospective forecasts made weekly from September 2022 to April 2024, INFLAenza's forecasts performed 41.7% better than the baseline model for COVID-19, 44% better for influenza and 40.6% better for RSV. These figures are relative improvements in weighted interval score, a metric that rewards accurate point forecasts and penalises intervals that are too wide or too narrow, so they describe improvement over a reference model rather than an absolute accuracy level.

Calibration, a separate question from accuracy, was reasonably close to nominal: the share of observed values falling inside the model's 95% prediction intervals was 94.5% for COVID-19, 88.5% for influenza and 96.7% for RSV. Influenza is the one where coverage fell furthest short of 95%, meaning its intervals were somewhat too narrow over the evaluation period.

Seasonality and spatial sharing both earn their place

The authors did not only compare against a baseline. They removed or altered components and re-ran the forecasts. Across the three diseases, INFLAenza outperformed a version giving each region its own separate seasonal effect by an average of 2.0%, a version giving each location its own independent seasonal effect by 7.7%, a version with no seasonal component by 10.8% and a version with no spatial connectivity by 7.9%. It also beat a standard SARIMA seasonal model by 33.3% across all diseases.

The pattern is informative about mechanism. Dropping seasonality costs the most, which fits a model whose main job is to learn a recurring annual shape from limited training data. Spatial sharing matters less but still helps, and it helps most where neighbouring states genuinely move together, as the COVID-19 correlation figures suggest. The regional-seasonal variant, which groups states into four Census regions plus separate effects for Hawaii, Alaska and Puerto Rico, comes closest to the full model, implying that much of the spatial benefit can be captured by coarser grouping.

Real-time forecasts are harder than reanalysis

In the live 2023-2024 FluSight challenge, INFLAenza was the top individual model, with an average relative weighted interval score of 0.76, behind the FluSight ensemble at 0.73 and one other individual model at 0.61. Against the ensemble it fell short by 1.3%, 2.7%, 4.2% and 8.5% at the one-, two-, three- and four-week horizons respectively, and error decomposition attributed the growing gap mainly to underprediction during the ascending phase of the epidemic.

The authors also quantify a gap between live and retrospective performance. Retrospective influenza forecasts improved on the baseline by 42%, versus 25% in real time; after harmonising time frame, horizons, locations and scoring, retrospective forecasts still outperformed real-time ones by 8.2%. The paper attributes this to real-time forecasting having to anticipate reporting delays that distort recently observed counts, and suggests coupling the model to a nowcasting component as a remedy. This is an author explanation, not something the evaluation isolates experimentally.

Distinct local seasonality is the main failure mode

At state level during the 2023-2024 influenza season, INFLAenza matched or beat the baseline for 90.4% of states and matched or beat the ensemble for 50%. The three largest performance gaps were Puerto Rico, Alaska and Arkansas. In Puerto Rico and Alaska the model produced considerably wider prediction intervals than the ensemble early in the season and overpredicted peak timing and magnitude; the authors link this to an early version that connected these isolated locations to the continental US, and to their seasonality differing from the rest of the country. In Arkansas, a prolonged shoulder deviated from other states' trends and was not captured by either the seasonal or the location-specific effects.

Across the full retrospective set, INFLAenza beat the baseline for all diseases and regions except RSV in Georgia and influenza in Puerto Rico, again attributed to distinct underlying seasonal dynamics. For COVID-19, performance was better in the Southeast and Northeast than in the West and Midwest, a pattern the authors trace to the 2022-2023 season, when Midwest and Western states peaked earlier and had a prolonged spring shoulder while Southern states tracked the national trend. The practical reading is that the model's portability depends on a location's season resembling the pool it is pooled with.

Inferred effects describe burden, not just forecasts

Because the model estimates its components, the authors use the posterior distributions to describe the three diseases. The seasonal effect quantifies when and how sharply each epidemic rises and falls, and the paper reports the timing and shape for influenza and RSV plus a biannual pattern for COVID-19. The location intercepts estimate whether a state's hospitalisation rate sits above or below the national average across its whole time series.

These intercepts show influenza burden varying more across states than COVID-19 or RSV: 81% of influenza states had 95% credible intervals containing zero, compared with 96% for COVID-19 and 100% for RSV. For influenza, the paper reports strong support for higher rates in the South and moderate support for lower rates in the Northeast and Pacific West; for COVID-19, moderate support for lower rates in the Northeast. Posterior mean intercepts correlated at 0.42 between COVID-19 and influenza, 0.61 between influenza and RSV and 0.70 between COVID-19 and RSV, suggesting states with high burden of one disease tend to have high burden of the others. The authors caution that these correlations ignore uncertainty in the intercepts and the short-term interaction component.

Choose it for breadth, not for beating the ensemble

The paper's own comparison sets the priority. INFLAenza is not the most accurate forecaster in the FluSight field: the ensemble scored better, and one individual model scored better still in 2023-2024. What it offers is near-parity with the ensemble from a single configuration applied unchanged to three pathogens with different dynamics, plus speed, since forecasts are produced in minutes. The authors' deployment guidance follows from the ablations: at least two representative seasons of training data to estimate the seasonal effect, and better performance when forecast units are connected, correlated and have few gaps, which is why all states for COVID-19 worked better than 12 geographically scattered states for RSV.

The clearest boundary is seasonality that does not resemble the pooled pattern. Puerto Rico, Alaska, Arkansas and Georgia are the documented cases where the shared seasonal and spatial structure misled the forecast, and the authors' suggested fixes are modest tuning of the short-term variance priors when counts are low and redefining the neighbourhood graph around mobility or contact rather than shared borders. Extending to dengue or malaria, which the paper proposes, would test exactly that boundary, since those systems are not evaluated here. The decision rule the evidence supports is therefore conditional: prefer this model when a new setting has at least two seasons of data and a season broadly shared with its neighbours, and expect the ensemble or a bespoke model to hold the edge where local timing diverges.

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