A Temporal-Dynamic Neural-SIR Approach based on LSTM for Stochastic Infectious Disease Forecasting

Accurate forecasting of infectious disease out-breaks is crucial for timely public health interventions and optimized resource allocation. Unlike traditional epidemiological models such as the Susceptible-Infected-Recovered (SIR) framework, which fail to capture real-world variability and uncertainty, recent hybrid models that combine mathematical modeling with machine learning (ML) techniques have shown promising results in epidemic forecasting. However, these models' ability to generalize to new uncertain scenarios remains underexplored, raising concerns about their reliability, robustness, and epidemiological interpretability.This paper presents Neural-SIR, a temporal-dynamic simulation-based framework that explores stochastic dynamics in disease modeling using SIR differential equations (DEs), to evaluate the ability of ML models to generalize. To capture the variability in temporal disease dynamics, our simulation-based framework generates synthetic data using two uncertainty modeling approaches. The first models inter-regional heterogeneity by randomly sampling the transition rates within a uniform distribution, and the second captures intra-population variability by incorporating random, temporal fluctuations through stochastic SIR DEs. Using the generated temporal data, we train multiple Long Short-Term Memory (LSTM) models with different architectures, and evaluate their performance using the Mean Absolute Error (MAE), Root Mean Squared Error (RMSE), and the Coefficient of Determination R². This approach allows us to rigorously determine each model's generalization ability in new, uncertain scenarios. Our findings indicate that by integrating stochastic dynamics, Neural-SIR incorporates the uncertainty that characterizes real-world scenarios, hence provides a rigorous and interpretable framework for evaluating the reliability and robustness of epidemic forecasting modeling approaches under uncertainty.Clinical relevance - Reliable and robust epidemic forecasting enables clinicians and public health professionals to antic-ipate disease outbreak severity, deploy timely region-specific interventions, and optimize resource allocation. This study introduces Neural-SIR, a temporal-dynamic framework that evaluates the reliability and robustness of epidemic forecasting and modeling approaches against inter-regional heterogeneity and intra-population variability, supporting better decision making in real-world healthcare settings.