Aug 2026· Model Assisted Statistics and Applications· 0 citations· 8 references
TL;DR
This work proposes MechGNN-Epi, a hybrid framework that couples a spatiotemporal graph encoder with a differentiable SIR update that yields epidemiologically constrained trajectories and produces region- and time-indexed parameter proxies that can be inspected as diagnostic signals, while not being guaranteed as causally identifiable mechanistic parameters.
Abstract
Mechanistic compartmental models such as SIR provide interpretability and enforce conservation of population, but their predictive performance can degrade in heterogeneous settings where transmission varies over time and across regions. Conversely, spatiotemporal graph neural networks (GNNs) can learn flexible spatial interactions from data, yet unconstrained predictors may yield epidemiologically inconsistent dynamics.
We propose MechGNN-Epi, a hybrid framework that couples a spatiotemporal graph encoder with a differentiable SIR update. Rather than directly predicting future infections, the model learns region- and time-specific transmission and recovery parameters from graph-based latent representations and then propagates compartments through a mechanistic solver. This design yields epidemiologically constrained trajectories and produces region- and time-indexed parameter proxies that can be inspected as diagnostic signals, while not being guaranteed as causally identifiable mechanistic parameters. We evaluate the pipeline on U.S. state/territory COVID-19 surveillance data using strict chronological splits and report variability across multiple random seeds, multi-horizon rollouts, and ablation/sensitivity studies against graph and model variants.
The SARS-CoV-2 pandemic highlighted the ongoing risk infectious diseases pose to society and the value of reliable information on the likely future burden. When forecasting an epidemic at fine spatial resolution, traditionally used mechanistic compartmental model struggle to capture highly complex granular transmission dynamics, resulting in inaccurate and overconfident forecasts. However, detailed Agent-Based Models (ABMs), are challenging to calibrate and are too computationally expensive to use in real-time. Amortized simulation-based inference promises to overcome this difficulty by exploiting the power of machine learning (ML) to perform approximate forecasting at near-real-time using arbitrarily complex models of epidemics. In this work we introduce Generative Neural Inference for Epidemics (GENIE), a spatio-temporal ML-based framework for high-resolution forecasting of the burden of respiratory pathogens. GENIE is designed to reflect two key characteristics of outbreaks: (i) shared biological mechanisms across locations and (ii) location-specific characteristics affecting transmission dynamics. This results in the model architecture having two modules: (i) a Local Infection Encoder - which learns to represent disease dynamics shared across all locations and (ii) a Local Profile Encoder - which learns location-specific representations. Using simulations from a high-resolution spatio-temporal ABM, GENIE is trained to generate samples from an approximate posterior predictive distribution of future epidemic trajectories. Benchmarked against established statistical and ML models, GENIE demonstrates superior performance across a range of measures including the timing and magnitude of peak hospitalisations.
Laura M Guzman-Rincon, George R.E. Bradley, Joel Kandiah et al.· 0 citations
Perturbation-omics experiments usually measure only a subset of molecular feature, intervention and time space, leaving many response trajectories, perturbation effects and disease- or differentiation-associated transitions unobserved. Here we present MEGA-ODE, a graph-constrained continuous-time framework for reconstructing sparse dynamic omics landscapes, predicting unmeasured molecular states and prioritizing virtual perturbations toward defined biological endpoints. MEGA-ODE integrates molecular-network priors, graph neural ordinary differential equations and context-adaptive mixture-of-experts routing. In L1000 transcriptomic perturbations and CPPA proteomic drug-response data, MEGA-ODE improved held-out-feature and unseen-perturbation prediction over baseline methods, and in SARS-CoV-2 infection time-series data it remained competitive for future-time-point forecasting. In a COVID-19 patient cohort, predicted intermediate profiles improved retrospective disease-stage stratification relative to observed profiles alone, while expert programs highlighted immune and inflammatory signals associated with severity. Across the MAPK drug-response and stem-cell differentiation case studies, graph- and expert-level attributions prioritized perturbation-associated MAPK edges, developmental regulators and TF-target relationships supported by independent promoter-proximal ChIP-seq overlap. In hESC-to-definitive-endoderm differentiation, MEGA-ODE prioritized candidate transcription-factor perturbations predicted to shift 12-36 h profiles toward 96 h definitive-endoderm marker signatures, framing trajectory navigation as a concrete hypothesis-generation task. Together, these results support biologically structured continuous-time modeling for prediction, interpretation and virtual-perturbation prioritization from sparse temporal omics data.
Infectious disease outbreaks strain medical resources and public-health systems, making accurate multi-horizon, multi-regional forecasting essential for early warning and resource allocation. Existing approaches face a trade-off: data-driven deep models can capture nonlinear spatiotemporal patterns but often overlook transmission mechanisms, whereas mechanistic models are interpretable but limited in modeling complex regional dependencies. To address this challenge, we propose Epidemic Spatial–Temporal Large Language Model (EpiSTLLM), which is a graph-structure-enhanced large language model for multi-regional infectious disease forecasting. EpiSTLLM injects regional adjacency information into Transformer-based representation learning to capture cross-regional transmission structure and long-term temporal dependencies. A temporal-gated cross-attention module generates horizon-specific latent transmission and recovery parameters, while a latent-space SIR-inspired propagation mechanism with a residual correction branch enables stable multi-horizon forecasting without requiring fully observed compartmental states. Experiments on the FluView state-level influenza-like illness dataset and NHSN state-level influenza hospitalization dataset show that EpiSTLLM achieves the best or highly competitive performance in most evaluation settings against statistical, deep learning, graph-based, and mechanism-guided baselines across 4-, 8-, and 12-week horizons. For example, EpiSTLLM reduces MAE and RMSE values by 9.5% and 6.2% at H=4 on FluView, and by 12.0% and 13.1% at H=8 on NHSN compared with the strongest baselines, respectively.
Siru Chen, Xuhao Guo, Zige Liu et al.· Mathematics· 0 citations
Regional surveillance data reflect local transmission, reporting, seeding, and external infection pressure, which are difficult to identify separately. We introduce GeoID-PINN, a physics-informed neural network (PINN) for susceptible-infectious-recovered-deceased (SIRD) dynamics. The model represents spatial dependence with a row-stochastic source-composition matrix whose rows assign nonnegative source weights that sum to one. We regularize this matrix toward a spatial prior constructed from distance, adjacency, commuting, or lead-lag information. In a four-region simulation with known truth, a compatible distance prior gives source-composition error 0.099. The error rises to 0.159 without regularization and 0.577 under a strongly misspecified prior, while trajectory fit and transmission-scale estimates remain similar. Accurate trajectories therefore do not guarantee recovery of the regional dependence structure. We also evaluate GeoID-PINN retrospectively using COVID-19 data from 64 Louisiana counties. Relative to an autoregressive negative-binomial baseline, Forecast-Trained Geo-PINN reduces mean squared error (MSE) from 32,957 to 11,468 and mean absolute error (MAE) from 70.60 to 57.73. The baseline has lower negative log likelihood (NLL), 5.158 versus 5.346, indicating better distributional fit but worse point accuracy. In a controlled 15-county comparison, county adjacency reduces MSE by 6.85 percent and MAE by 3.1 percent. Similar performance across plausible priors supports structured regularization but not unique edge recovery. These results require prior-sensitivity and observation-model checks before interpretation.
We introduce a hybrid computational framework for the automated discovery of complex dynamic regimes in spatially distributed epidemiological models. Traditional models often fail to capture the rich spatio-temporal heterogeneity of disease spread, while high-dimensional Partial Differential Equation (PDE) models suffer from the “curse of dimensionality” during parameter calibration. To address this, we couple a Differential Evolution (DE) search engine with a Just-In-Time (JIT) compiled Finite Difference solver, resulting in a hybrid architecture that performs “Simulation-Based Inference”. This method navigates the parameter space to identify regimes that generate specific emergent behaviors, such as Turing patterns, traveling wave competition, and resonance-driven outbreaks. We apply our method to a spatial Susceptible-Infected-Recovered-Susceptible (SIRS) model featuring seasonal forcing and heterogeneous diffusion. Our results demonstrate that the JIT-compiled solver achieves a $\sim 9 \times$ speedup compared to vectorized NumPy implementations, rendering the evolutionary exploration of PDEs computationally feasible and validating the system's ability to discover worst-case epidemic scenarios and geometric interference patterns without reliance on manual analytical derivation.
Olha Sirikova, I. Vergunova· 2026 6th International Confe...· 0 citations
Infectious diseases exhibit complex and rapidly evolving transmission dynamics, requiring modeling approaches that can accurately capture these mechanisms. The SIRS-D compartmental model provides a suitable framework, as it incorporates temporary immunity and disease-induced mortality within the epidemic process. Accurate parameter estimation is essential for quantifying the transmission rate, recovery rate, waning immunity rate, and mortality rate, which collectively govern the system behavior. Among existing estimation methods, Physics-Informed Neural Networks (PINNs) offer significant advantages by integrating observational data with the underlying structure of differential equations, thereby preserving physical consistency while maintaining robustness under imperfect data conditions. In this study, PINNs are employed to estimate the parameters of the SIRS-D model using synthetic data generated through the fourth-order Runge–Kutta (RK4) method to ensure stable and consistent numerical solutions. To better represent real-world measurement conditions, 5% noise is added to the synthetic data, introducing realistic variability into the training process. The results demonstrate that PINNs successfully reconstruct the trajectories of S(t), I(t), R(t), and D(t) with low prediction errors. The model achieves MAE values of 0.0065 (S), 0.0067 (I), 0.0208 (R), and 0.0043 (D), with corresponding RMSE values of 0.0090, 0.0074, 0.0253, and 0.0058. Moreover, the estimated parameters closely match the true values, yielding ????????=0.5031, ????=0.0996, ????=0.0095, and ????=0.0149, demonstrating strong parameter identification capability. These findings confirm that PINNs constitute a reliable and accurate framework for analyzing infectious disease dynamics and offer promising potential for extension to more complex epidemiological models and real-world datasets.
Fitri Cahyani, Abdurakhman Abdurakhman, Chyntia Meininda Anjanni· The eurasia proceedings of s...· 0 citations