Neural Ordinary Differential Equations for Modeling Epidemic Spreading

Mathematical models of infectious diseases have long been used for studying the mechanisms by which diseases spread, for predicting the spread of epidemics, and also for controlling their outbreaks. These models are based on some assumptions and different assumptions give rise to different models. Models on social networks of individuals which capture contact patterns are usually more realistic and can more accurately model contagion dynamics. Unfortunately, computing the output of realistic models is often hard. Thus, modeling the evolution of contagion dynamics over large complex networks constitutes a challenging task. In this paper, we present a computational approach to model the contagion dynamics underlying infectious diseases. Specifically, we focus on the susceptible-infectious-recovered (SIR) epidemic model on networks. Given that this model can be expressed by an intractable system of ordinary differential equations, we devise a simpler system that approximates the output of the model. Then, we capitalize on recent advances in neural ordinary differential equations and propose a neural architecture that can effectively predict the course of an epidemic on the network. We apply the proposed architecture on several network datasets and compare it against state-of-the-art methods under different experimental settings. Our results indicate that the proposed method improves predictions in various spreading scenarios, paving the way for the extensive application of interpretable neural networks in the field of epidemic spreading. At the same time, the proposed model is highly efficient even when trained on very large networks where traditional algorithms become significantly slower.