Towards inferring network properties from epidemic data

TL;DR

This paper investigates the use of mean-field network models, specifically the PWM with SIR, for inferring disease and network parameters from epidemic data, comparing MLE and DSA methods in simulated and real-world scenarios.

Contribution

It demonstrates that network-based mean-field models can be used to infer disease and network parameters, highlighting the robustness of DSA over MLE in real-world data.

Findings

Dynamical survival analysis (DSA) is more robust than MLE for real-world epidemic data.

Mean-field models can approximate likelihoods for parameter inference.

Network models provide insights into underlying epidemic and network properties.

Abstract

Epidemic propagation on networks represents an important departure from traditional massaction models. However, the high-dimensionality of the exact models poses a challenge to both mathematical analysis and parameter inference. By using mean-field models, such as the pairwise model (PWM), the complexity becomes tractable. While such models have been used extensively for model analysis, there is limited work in the context of statistical inference. In this paper, we explore the extent to which the PWM with the susceptible-infected-recovered (SIR) epidemic can be used to infer disease- and network-related parameters. The widely-used MLE approach exhibits several issues pertaining to parameter unidentifiability and a lack of robustness to exact knowledge about key quantities such as population size and/or proportion of under reporting. As an alternative, we considered the recently developed dynamical survival analysis (DSA). For scenarios in which there is no model mismatch, such as when data are generated via simulations, both methods perform well despite strong dependence between parameters. However, for real-world data, such as foot-and-mouth, H1N1 and COVID19, the DSA method appears more robust to potential model mismatch and the parameter estimates appear more epidemiologically plausible. Taken together, however, our findings suggest that network-based mean-field models can be used to formulate approximate likelihoods which, coupled with an efficient inference scheme, make it possible to not only learn about the parameters of the disease dynamics but also that of the underlying network.