Finding Patient Zero: Learning Contagion Source with Graph Neural Networks

Abstract

Locating the source of an epidemic, or patient zero (P0), can provide critical insights into the infection's transmission course and allow efficient resource allocation. Existing methods use graph-theoretic centrality measures and expensive message-passing algorithms, requiring knowledge of the underlying dynamics and its parameters. In this paper, we revisit this problem using graph neural networks (GNNs) to learn P0. We establish a theoretical limit for the identification of P0 in a class of epidemic models. We evaluate our method against different epidemic models on both synthetic and a real-world contact network considering a disease with history and characteristics of COVID-19. We observe that GNNs can identify P0 close to the theoretical bound on accuracy, without explicit input of dynamics or its parameters. In addition, GNN is over 100 times faster than classic methods for inference on arbitrary graph topologies. Our theoretical bound also shows that the epidemic is like a ticking clock, emphasizing the importance of early contact-tracing. We find a maximum time after which accurate recovery of the source becomes impossible, regardless of the algorithm used.

Inferring Spatial Source of Disease Outbreaks using Maximum Entropy

“…Current understanding of epidemic dynamics, suggests that contact-tracing is effective only in the initial stages of the outbreak, and any information on the infection source is lost at later times. Indeed, in [51] an approximation to this temporal horizon, t hor , was derived for the SIR model. Adapting the formulation to the SEAIR model, leads to an expression of the form:…”

“…Specifically, we test the accuracy of identifying the correct spatial origin of the infection-seed as we increase the number of counties observed. We choose three counties with different population densities in which to seed the infection: B) and beyond the time horizon (t hor ), where t hor (adapted from [51]), is a reported fundamental limit beyond which no algorithm can detect the true origin of infection.…”

“…For the sake of comparison, we now compute the t hor value for our compartmental model, according to the rationale followed in [51]. Mathematically, the authors define the time horizon as the time at which the number of infectious individuals, whose evolution is assumed to follow the early stage dynamics of the outbreak, scales to the entire population.…”

“…Other approaches include generalized profiling [40], approximate Bayesian computation [41][42][43], derivative-free optimization [44,45] and Bayesian inference [46][47][48][49][50]. Furthermore, most of the epidemiological models in the literature focus on forward dynamics of the diffusion of the pathogen through the network, while the backward-dynamics problem of identifying the diffusion source has been comparatively less studied [51][52][53]. Such an analysis bears significant importance in guiding systematic contact-tracing and increasing the chance of early containment of an outbreak.…”

“…c) Accuracy vs mid-point observation period. Model's accuracy drops as observations are obtained from time values beyond early stages of the outbreak (stage A) but increases again at more advanced time periods (stageB) and beyond the time horizon (t hor ), where t hor (adapted from[51]), is a reported fundamental limit beyond which no algorithm can detect the true origin of infection.…”