A data augmentation strategy for deep neural networks with application to epidemic modelling

TL;DR

The paper tackles the need for scalable and accurate epidemic forecasting by marrying mechanistic SIR-type dynamics with data-driven surrogates. It augments real COVID-19 data with synthetic trajectories from a social-SIR model with saturated incidence $H(t,I)$ to train FFNs and NARs, offering a practical alternative to PINNs. The key contributions are a two-phase parameter estimation regime for pre- and post-lockdown dynamics and a data-augmentation framework that improves temporal forecasting via NARs, demonstrated on Italy and Spain during lockdown. This hybrid approach enables fast, data-informed predictions while retaining interpretability from the mechanistic backbone, with potential to inform public health decisions under data scarcity or uncertainty.

Abstract

In this work, we integrate the predictive capabilities of compartmental disease dynamics models with machine learning ability to analyze complex, high-dimensional data and uncover patterns that conventional models may overlook. Specifically, we present a proof of concept demonstrating the application of data-driven methods and deep neural networks to a recently introduced Susceptible-Infected-Recovered type model with social features, including a saturated incidence rate, to improve epidemic prediction and forecasting. Our results show that a robust data augmentation strategy trough suitable data-driven models can improve the reliability of Feed-Forward Neural Networks and Nonlinear Autoregressive Networks, providing a complementary strategy to Physics-Informed Neural Networks, particularly in settings where data augmentation from mechanistic models can enhance learning. This approach enhances the ability to handle nonlinear dynamics and offers scalable, data-driven solutions for epidemic forecasting, prioritizing predictive accuracy over the constraints of physics-based models. Numerical simulations of the lockdown and post-lockdown phase of the COVID-19 epidemic in Italy and Spain validate our methodology.

Figures (6)

• Figure 1: Pre-lockdown phase. Dynamics of the infected population computed by solving the social-SIR model \ref{['eq:deterministicSIR_H']} with $\beta$ and $\gamma$ as in \ref{['eq:beta_gamma_est']} (Italy), and as in \ref{['eq:beta_gamma_est_spain']} (Spain) and $H(t,I(t))=1$, compared with the experimental data. In the embedded plot the pointwise error between the two quantities computed as in \ref{['eq:error']}. On the left, Italy. On the right, Spain.
• Figure 2: Lockdown and post-lockdown phase. On the left the dynamics of the infected population computed by solving the generalized SIR model \ref{['eq:deterministicSIR_H']} with $\beta$ and $\gamma$ as in \ref{['eq:beta_gamma_est']} (Italy), and as in \ref{['eq:beta_gamma_est_spain']} (Spain), assuming the contact function $H$ to be defined as in \ref{['eq:H_instaneous']} and, alternatively, with the smoothed version \ref{['eq:smoothing_projection']} setting $k=1.6$ compared with the experimental data. In the embedded plot the pointwise error between the two infected populations computed as in \ref{['eq:error']}. On the right the contact function $H$ computed as in \ref{['eq:H_instaneous']} and its smoothed version computed introducing an operator as in \ref{['eq:smoothing_projection']}. First row, Italy. Second row, Spain.
• Figure 3: Feedforward neural network for Italy. On the left the dynamics of the infected population computed by training a FNN on real and synthetic data and tested over the train interval $[t_l,T]$ compared to the available data. On the right the solution computed with the same FNN tested over the time interval $(T,T_{test}]$ compared to the available data. Embedded the error between the available data test and the neural network solution computed as in \ref{['eq:error']}.
• Figure 4: Feedforward neural network for the Spain case. On the left the dynamics of the infected population computed by training a FNN on real and synthetic data and tested over the train interval $[t_l,T]$ compared to the available data. On the right the solution computed with the same FNN tested over the time interval $(T,T_{test}]$ compared to the available data. Embedded the error between the available data test and the neural network solution computed as in \ref{['eq:error']}. First row, Italy. Second row, Spain.
• Figure 5: Nonlinear autoregressive network: training data. Solution obtained by training a NAR network on both real and synthetic data, then testing it on the same dataset and comparing it to the available data. On the left, the case for Italy, and on the right, the one for Spain.