Hybrid Forecasting Model Sharpens Predictions of Seasonal Influenza Waves in China

Influenza remains one of the most predictable yet persistently disruptive infectious diseases in the world, arriving each year with enough regularity to be anticipated and enough variability to catch health systems off guard. A new epidemiological study from Jiande, a county-level city within Hangzhou in eastern China’s Zhejiang Province, offers a detailed look at how laboratory-confirmed influenza A and B cases behave over time and, more importantly, how their future trajectories might be forecast with greater precision. The research, published in BMC Infectious Diseases by Fenglong Zhu and Guisheng Liu of the First People’s Hospital of Jiande together with Cong Huang of Panzhihua Central Hospital, describes a hybrid statistical and machine-learning approach that combines two very different modelling traditions into a single forecasting engine.

The study rests on a deceptively simple foundation: six years of hospital-based surveillance data. The researchers extracted records of laboratory-confirmed positive influenza A and B cases spanning January 2019 through December 2024 from the medical-record registration system at the Jiande Branch of the Second Affiliated Hospital of Zhejiang University School of Medicine. Because the data were drawn from routine diagnostic testing rather than sentinel sampling or syndromic estimates, they represent a direct count of virologically confirmed infections presenting to a single healthcare institution. That characteristic gives the series a certain fidelity, though it also means the counts reflect the population that sought care and tested positive at that hospital rather than the true incidence of influenza in the wider community.

Before any forecasting could begin, the team characterised the epidemiological rhythm embedded in the data. The analysis revealed distinct seasonal patterns for both influenza types, with epidemic peaks occurring predominantly in winter and spring. This seasonality is the classic signature of influenza in temperate and subtropical regions, driven by a combination of factors including humidity and temperature, human behaviour that concentrates people indoors during colder months, and the survival characteristics of the virus itself in aerosols and on surfaces. Knowing that the seasonal wave will come is one thing; knowing how large it will be and when exactly it will crest is quite another, and that is precisely the gap the authors set out to narrow.

The first half of the hybrid model is the seasonal autoregressive integrated moving average model, or SARIMA, a workhorse of classical time-series analysis. SARIMA models describe a series as a function of its own past values, past forecast errors, and seasonal counterparts of both, after differencing the data to achieve stationarity. In this study, the model structure was selected systematically: the authors examined autocorrelation and partial autocorrelation functions and applied formal stationarity tests including the Augmented Dickey-Fuller and Kwiatkowski-Phillips-Schmidt-Shin procedures, with model adequacy judged by information criteria such as the Akaike and Bayesian information criteria. The search converged on a SARIMA(1, 0, 1)(2, 1, 1) with a seasonal period of four for influenza A, and a SARIMA(3, 0, 0)(2, 1, 1) with the same seasonal period for influenza B. The quarterly seasonal differencing captured the annual epidemic cycle compressed into the monthly series, while the autoregressive and moving-average terms handled short-term dependencies within and between seasons.

SARIMA models excel at capturing regular, repeating structure, but they are fundamentally linear: they assume that future values relate to past values through fixed linear coefficients. Real epidemic curves are rarely so well behaved. Transmission intensity shifts as susceptible populations deplete, as schools open and close, and as viral evolution produces antigenic drift. The second half of the hybrid, the long short-term memory network, addresses this limitation. LSTM is a form of recurrent neural network designed to learn long-range dependencies in sequential data through gated memory cells that decide what information to retain, update, or discard at each time step. Where SARIMA imposes a rigid mathematical structure, LSTM learns flexible, potentially nonlinear mappings from past observations to future values, making it well suited to the irregularities that a seasonal statistical model smooths over.

The hybrid SARIMA-LSTM architecture used here follows a logic of decomposition and residual learning. The SARIMA component first models the predictable seasonal and linear structure of the case-count series. What remains after SARIMA has done its work, the residual component, contains the nonlinear and irregular dynamics that the classical model cannot express. The LSTM is then trained on this residual signal, learning to correct the SARIMA forecast rather than to reproduce the entire series from scratch. The two components are finally recombined so that the seasonal backbone supplied by SARIMA is refined by the neural network’s learned corrections. The full model was implemented in MATLAB R2024a, and the authors have made core code snippets available as supplementary material, a small but meaningful contribution to reproducibility in a field where methodological details are often opaque.

To judge whether the added complexity was worthwhile, the researchers held out the 2024 data as an out-of-sample test set, allowing each model to forecast a full year it had never seen. Performance was measured with two standard error metrics: mean absolute error, which captures the average magnitude of forecast mistakes, and root mean square error, which penalises large errors more heavily. The results were consistent across both influenza types. For influenza A, the hybrid model reduced mean absolute error by 7.3 percent and root mean square error by 7.1 percent relative to standalone SARIMA, and achieved a 9.4 percent reduction in mean absolute error and a 4.6 percent reduction in root mean square error relative to standalone LSTM. For influenza B, the improvements were similar or larger: a 7.5 percent reduction in both error metrics compared with SARIMA, and reductions of 8.9 percent in mean absolute error and 9.5 percent in root mean square error compared with LSTM.

One secondary finding deserves particular attention: the hybrid model performed better for influenza B than for influenza A. The authors note this explicitly, and it is biologically plausible. Influenza B tends to exhibit more regular and less genetically volatile epidemic behaviour than influenza A, which is subject to more frequent antigenic drift and occasional shift and can produce earlier or more erratic season onsets. A forecasting framework that leans on stable seasonal structure, as the SARIMA backbone does, will naturally fare better with a pathogen whose dynamics are themselves more stable. Influenza A’s greater unpredictability leaves more residual noise for any model, hybrid or otherwise, to struggle with, and the smaller margin of improvement for influenza A against the standalone LSTM hints at that ceiling.

The practical implications extend beyond the metrics. Local healthcare institutions and disease-control agencies operate under real constraints: vaccine campaigns must be timed, antiviral stockpiles allocated, staff rosters adjusted, and hospital beds and testing capacity planned months in advance. A model that reliably trims forecast error by roughly seven to nine percent, even on monthly case counts from a single hospital, translates into earlier and more accurate warnings of when the seasonal wave will build and peak. The authors position the model as an auxiliary reference rather than a replacement for expert judgement, which is the appropriate framing: hospital-derived positive case counts are influenced by testing practices and care-seeking behaviour, and any forecast built on them inherits those biases. Still, as a complement to national sentinel systems, a locally trained model grounded in the actual case flow of a specific institution offers a granularity that broad regional surveillance cannot.

The study also illustrates a broader trend in infectious-disease modelling: the convergence of classical statistical methods and machine learning into hybrid frameworks that play to the strengths of each. Purely statistical models remain interpretable and data-efficient; neural networks capture nonlinearities but demand more data and careful regularisation. Combining them, as this Jiande team has done with a modest six-year dataset, shows that useful gains do not require enormous data volumes or exotic architectures, only a thoughtful division of labour between the two approaches. As climate variability, post-pandemic shifts in respiratory-virus circulation, and evolving vaccination patterns continue to perturb the once-reliable rhythm of influenza seasons, tools that squeeze additional accuracy out of routine surveillance data will only grow in value for the clinicians and public-health officials who must act on their predictions.

Subject of Research: Hybrid SARIMA-LSTM time-series forecasting of laboratory-confirmed influenza A and B case counts from hospital surveillance data in Jiande, Hangzhou, China

Article Title: Forecasting influenza A and B positive case counts using a hybrid seasonal autoregressive integrated moving average and long short-term memory (SARIMA-LSTM) model: an epidemiological study from Jiande, Hangzhou, China

Article References: Zhu, F., Liu, G., & Huang, C. (2026). Forecasting influenza A and B positive case counts using a hybrid seasonal autoregressive integrated moving average and long short-term memory (SARIMA-LSTM) model: an epidemiological study from Jiande, Hangzhou, China. BMC Infectious Diseases. https://doi.org/10.1186/s12879-026-14587-7

Image Credits: AI Generated

DOI: 10.1186/s12879-026-14587-7

Keywords: influenza A, influenza B, SARIMA-LSTM hybrid model, time-series forecasting, epidemiology, seasonality, machine learning, LSTM neural network, hospital surveillance, BMC Infectious Diseases, China, public health