The research team, led by Antonio Gondim and including Chidozie Chukwu, Folashade Agusto, and Joshua Ologbonyo, built their analysis around a cumulative case series constructed from annual measles surveillance records. Rather than modeling yearly incidence alone, they tracked the total number of cases accumulated over time, a measure that permanently retains the effects of major outbreaks. This approach allowed them to quantify how resurgences in 2014, 2019, and 2025 produced lasting upward shifts in national measles burden. The cumulative trajectory, because it increases monotonically and each annual value differs from the previous one by a comparatively small increment, forms a smooth curve that statistical models can track with high precision during stable periods.

Four forecasting frameworks were compared: a Poisson generalized linear model, a quasi-Poisson GLM, a negative binomial GLM, and an ARIMAX grid-search model. The count-regression models use a log-linear mean structure with a baseline time trend and cumulative outbreak-shift indicators for 2014, 2019, and 2025. These indicators capture the fact that once cases occur during an outbreak year, they remain part of the cumulative total in all later observations. The ARIMAX model, by contrast, combines a regression mean with an autoregressive error process, allowing recent annual activity to inform short-term predictions. The researchers selected the ARIMAX specification through an explicit grid search over candidate orders rather than automatic stepwise selection, ultimately choosing a model with two autoregressive terms.

The three count-regression models produced nearly identical parameter estimates and fitted trajectories. The estimated outbreak-shift coefficients were all positive and statistically significant, corresponding to multiplicative increases of approximately 1.1 percent for 2014, 1.8 percent for 2019, and 2.9 percent for 2025 on the cumulative baseline. The quasi-Poisson model estimated a dispersion parameter of roughly 0.11, indicating pronounced underdispersion relative to the Poisson variance assumption. This result is a structural consequence of modeling cumulative rather than incident counts: the smooth, monotonically increasing trajectory exhibits far less year-to-year variability than a Poisson distribution with a large cumulative mean would imply. The negative binomial dispersion parameter was effectively zero and statistically insignificant, causing that model to collapse toward the Poisson specification.

The ARIMAX grid-search model told a different statistical story. Its two autoregressive terms were both statistically significant, indicating residual temporal dependence after accounting for the time trend and outbreak pulse. However, the one-year outbreak pulse indicator, which retained only the 2014 and 2025 pulses, was not statistically significant and carried a very wide confidence interval. The researchers attribute this imprecision to parameter-identifiability limitations: with only two outbreak pulses in a short annual series, the pulse effect is partially absorbed by the autoregressive terms and the estimated trend. A separate 2019 pulse was not retained because adding it produced unstable coefficients and inflated standard errors due to collinearity with the autoregressive dynamics.

In-sample accuracy strongly favored the count-regression models. The Poisson and quasi-Poisson models achieved a training mean absolute error of 64.60 cumulative cases and a root mean squared error of 83.85, while the negative binomial model performed almost identically. The ARIMAX model, with training MAE of 341.24 and RMSE of 499.82, appeared substantially weaker on historical fit. But the held-out 2026 validation reversed this ranking entirely. The researchers withheld the first four months of 2026 data from model fitting and used the observed partial-year cumulative total as a direct validation target. As of May 1, 2026, the cumulative count stood at 84,565 cases.

Every model fell short of that observation. The Poisson, quasi-Poisson, and negative binomial models all forecast approximately 82,842 cumulative cases for 2026, underestimating the observed total by roughly 1,723 cases. The ARIMAX model, though closer, still underpredicted by approximately 1,416 cases. On the annual-increment scale, the gap was even starker: the count-regression models implied only about 91 additional cases for 2026, while 1,814 cases had already been reported by May 1. The ARIMAX model implied roughly 398 cases, still far below the observed burden. The researchers supplemented this single-point validation with rolling one-year-ahead validation over the 2016–2025 test period, refitting each model using only data available before each test year. The count-regression models achieved lower MAE values in this exercise, while the ARIMAX model achieved a lower RMSE, indicating better performance in reducing larger forecast errors.

The systematic underprediction across all four models carries a clear epidemiological conclusion: the 2026 outbreak cannot be explained as a continuation of the 2025 outbreak effect alone. The forecasted annual burden was effectively reached within the first four months of the year, implying that the final 2026 cumulative burden will substantially exceed that of previous years. The researchers note that non-outbreak years in the training window averaged approximately 111 annual cases, with a maximum of 381, while the three documented resurgences reached 667 cases in 2014, 1,274 in 2019, and 2,285 in 2025. The 1,814 cases already reported by May 1, 2026 exceed the largest ordinary year more than threefold.

Based on these findings, the team proposes a simple, model-agnostic surveillance rule: introduce a new outbreak-year indicator when the observed annual incident count exceeds approximately 500 cases, about four times the recent non-outbreak average, corroborated where possible by an external public-health signal such as a CDC outbreak declaration. Because this threshold is descriptive of annual increments rather than requiring estimation of a pulse coefficient, it sidesteps the identifiability limitations that plagued the ARIMAX outbreak indicator. The researchers caution that the threshold is calibrated on a small number of resurgence years and should be recalibrated as additional outbreak years accrue.

The study highlights a fundamental tradeoff between explanatory and predictive performance in infectious disease forecasting. Count-regression models provide superior historical fit and direct epidemiological interpretation, quantifying how major outbreak periods produce persistent shifts in cumulative burden. Time-series models sacrifice some interpretability but gain the ability to adapt to recent trends and improve short-term forecasts. The researchers suggest that future forecasting efforts should incorporate a dedicated 2026 outbreak indicator or model the 2025–2026 period as a separate outbreak phase, and that accuracy may be further improved by adding covariates such as vaccination coverage, vaccine exemption rates, population mobility, and vaccine hesitancy. As the 2026 resurgence continues to unfold, the findings underscore that public health tracking must adapt to a heightened risk environment that historical patterns alone can no longer anticipate.

Subject of Research: Insights on United States cumulative measles cases during the 2026 outbreak using ARIMA and generalized linear models

Article Title: Insights on United States cumulative measles cases during the 2026 outbreak using ARIMA and generalized linear models

Article References: Gondim, A., Chukwu, C. W., Agusto, F. B., & Ologbonyo, J. (2026). Insights on United States cumulative measles cases during the 2026 outbreak using ARIMA and generalized linear models. Frontiers in Epidemiology, 6, Article 1921780. https://doi.org/10.3389/fepid.2026.1921780

Image Credits: AI Generated

DOI: 10.3389/fepid.2026.1921780

Keywords: Insights, United, States, cumulative, measles, cases, during, outbreak, ARIMA, generalized, linear, models