Universal nonlinear infection kernel from heterogeneous exposure on higher-order networks

TL;DR

This paper introduces a hypergraph-based model capturing complex, nonlinear infection dynamics due to heterogeneous environments and exposure, revealing phenomena like discontinuous transitions and super-exponential spread.

Contribution

It proposes a universal nonlinear infection kernel derived from heterogeneous exposure on higher-order networks, advancing epidemic modeling beyond linear assumptions.

Findings

Heterogeneous exposure induces a universal nonlinear infection relationship.

Nonlinear kernels lead to discontinuous epidemic transitions.

Emergence of super-exponential spread and hysteresis phenomena.

Abstract

The colocation of individuals in different environments is an important prerequisite for exposure to infectious diseases on a social network. Standard epidemic models fail to capture the potential complexity of this scenario by (1) neglecting the higher-order structure of contacts which typically occur through environments like workplaces, restaurants, and households; and by (2) assuming a linear relationship between the exposure to infected contacts and the risk of infection. Here, we leverage a hypergraph model to embrace the heterogeneity of environments and the heterogeneity of individual participation in these environments. We find that combining heterogeneous exposure with the concept of minimal infective dose induces a universal nonlinear relationship between infected contacts and infection risk. Under nonlinear infection kernels, conventional epidemic wisdom breaks down with the emergence of discontinuous transitions, super-exponential spread, and hysteresis.