Nonlinear bias toward complex contagion in uncertain transmission settings

TL;DR

This paper demonstrates that heterogeneity in transmission risks in complex contagion models can lead to superlinear infection dynamics, which may be mistaken for true complex contagion, emphasizing the importance of accounting for heterogeneity.

Contribution

It introduces a hypergraph-based epidemic model incorporating heterogeneous transmission rates and develops a Bayesian inference framework to detect nonlinearity in contagion processes.

Findings

Ignoring heterogeneity biases models toward superlinear regimes.

Superlinear infection rates can emerge from simple contagions due to heterogeneity.

Misclassification risks increase if heterogeneity is not considered.

Abstract

Current epidemics in the biological and social domains are challenging the standard assumptions of mathematical contagion models. Chief among them are the complex patterns of transmission caused by heterogeneous group sizes and infection risk varying by orders of magnitude in different settings, like indoor versus outdoor gatherings in the COVID-19 pandemic or different moderation practices in social media communities. However, quantifying these heterogeneous levels of risk is difficult and most models typically ignore them. Here, we include these novel features in an epidemic model on weighted hypergraphs to capture group-specific transmission rates. We study analytically the consequences of ignoring the heterogeneous transmissibility and find an induced superlinear infection rate during the emergence of a new outbreak, even though the underlying mechanism is a simple, linear contagion. The dynamics produced at the individual and group levels are therefore more similar to complex, nonlinear contagions, thus blurring the line between simple and complex contagions in realistic settings. We support this claim by introducing a Bayesian inference framework to quantify the nonlinearity of contagion processes. We show that simple contagions on real weighted hypergraphs are systematically biased toward the superlinear regime if the heterogeneity of the weights is ignored, greatly increasing the risk of erroneous classification as complex contagions. Our results provide an important cautionary tale for the challenging task of inferring transmission mechanisms from incidence data. Yet, it also paves the way for effective models that capture complex features of epidemics through nonlinear infection rates.