A novel Milstein-stochastic epidemiologically-informed neural network for approaching epidemic dynamics: Application to Mpox disease.

GENIE: Generative Neural Inference for Epidemics

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.

Physics-Informed Neural Networks (PINNs) for Parameter Estimation in the SIRS-D Epidemiological Model

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.

Fractional physics-informed neural network approach to inverse problems in epidemiological modeling

This study proposes a Fractional-Order Physics-Informed Neural Network (FPINN) framework for solving inverse parameter estimation problems in both fractional SIR and augmented SEIR epidemiological models and demonstrates that the proposed method accurately reconstructs epidemic trajectories and captures the influence of memory effects on disease evolution.

Boosted training strategy for physics-informed neural networks in modeling non-linear computer virus dynamics with vertical transmission

Computer-virus propagation in networked systems is often modeled by epidemic-type derivative equations. Still, standard quantitative solvers can become computationally demanding and may exhibit small stability for long-term predictions. This work develops a Physics-Informed Neural Network (PINN) based framework for an e-epidemic SI1I2R model of computer-virus spread that incorporates a possibly transmissible class, an amply transmissible class, and direct transmission, allowing nodes to be initially compromised without contact. The proposed PINN uses a multilayer, amply connected architecture with Swish-ReLU activations to approximate the solution to the coupled nonlinear common differential equations and to enforce the governing dynamics through a physics-based loss. We use standard error metrics such as Mean Squared Error (MSE), Theil’s Inequality Coefficient (TIC), and Mean Absolute Deviation (MAD) to compare the model's performance against a reference ODE Solver. We also examine training and validation loss profiles across several trials. A grid-based sensitivity analysis of key parameters (the infection rate and the progression rate from I1 to I2) is conducted to determine how they affect the peak sizes of infected and recovered populations. The results show that the PINN accurately reproduces the reference SI1I2R dynamics with low errors across all compartments. Swish-ReLU is the most stable and accurate training function of the ones that were tested. These results indicate that PINNs are a reliable and possibly resource-efficient way to model and predict how computer viruses spread. They also show that they could be useful for future AI-based epidemic modeling in cybersecurity.

A Fractional Physics-Informed Neural Network with Ensemble Learning for Dengue Forecasting

SUC–PINNs: A physics-informed neural networks approach to inverse problems in epidemic models with partial observability

Experiments with synthetic data and COVID-19 surveillance data show that SUC–PINN recovers plausible hidden infection trajectories, yields stable parameter estimates, and provides accurate short-term forecasts, support SUC–PINN as a practical computational approach for inverse modeling and prediction in partially observed epidemic dynamics.