How (Not) to Hybridize Neural and Mechanistic Models for Epidemiological Forecasting

TL;DR

This paper addresses the difficulty of epidemiological forecasting under partial observability and non-stationarity by proposing EpiNode, a hybrid neural–mechanical framework. EpiNode decomposes the observed infections into trend, seasonal, and residual components using Variational Mode Decomposition, then drives three Collaborated Latent Neural ODEs with time-delay-embedded controls, fused to decode bounded time-varying transmission, recovery, and immunity-loss rates that feed a mechanistic SIRS model. Across synthetic and real-world datasets, including seasonal and multi-wave regimes, EpiNode achieves 15–35% reductions in long-horizon RMSE, 1–3 weeks improvement in peak timing, and up to 30% reduction in peak-magnitude bias, outperforming strong baselines without external covariates. The method yields interpretable parameter trajectories and robust forecasts, highlighting the value of explicit non-stationarity modeling and multi-scale control signals in epidemiological forecasting.

Abstract

Epidemiological forecasting from surveillance data is a hard problem and hybridizing mechanistic compartmental models with neural models is a natural direction. The mechanistic structure helps keep trajectories epidemiologically plausible, while neural components can capture non-stationary, data-adaptive effects. In practice, however, many seemingly straightforward couplings fail under partial observability and continually shifting transmission dynamics driven by behavior, waning immunity, seasonality, and interventions. We catalog these failure modes and show that robust performance requires making non-stationarity explicit: we extract multi-scale structure from the observed infection series and use it as an interpretable control signal for a controlled neural ODE coupled to an epidemiological model. Concretely, we decompose infections into trend, seasonal, and residual components and use these signals to drive continuous-time latent dynamics while jointly forecasting and inferring time-varying transmission, recovery, and immunity-loss rates. Across seasonal and non-seasonal settings, including early outbreaks and multi-wave regimes, our approach reduces long-horizon RMSE by 15-35%, improves peak timing error by 1-3 weeks, and lowers peak magnitude bias by up to 30% relative to strong time-series, neural ODE, and hybrid baselines, without relying on auxiliary covariates.

Figures (20)

• Figure 1: EpiNode accuracy as a function of lookback window and forecast horizon.
• Figure 2: Failure of SIR forecasts from neural ODEs under full and partial observability at a train/forecast split of $0.2/0.8$. When all compartments $S(t), I(t), R(t)$ are observed (a), the neural ODE accurately recovers and extrapolates the epidemic dynamics. Under partial observability with only $I(t)$ available (b), the model fits the observed infections but exhibits drift in the unobserved compartments, leading to degraded long-horizon forecasts.
• Figure 3: Failure of SIR forecasts from AE-NODE under full and partial observability at a train/forecast split of $0.2/0.8$ with full-state supervision (a) and under I-only supervision (b).
• Figure 4: Failure of SIR forecasts from AE-NODE under short training windows, with bidirectional training.
• Figure 5: Incorporating physics informed losses. (a) with only $I(t)$ observed, forecasts are reasonable with an SIR model assumption (a) but are poor under an SIRS model (b).