Networked SIS Epidemics with Awareness

TL;DR

This paper models how awareness of an epidemic influences individual behavior and epidemic spread on networks, showing that awareness generally reduces infection levels and epidemic duration through stochastic and mean-field analyses.

Contribution

It introduces a coupled stochastic and mean-field framework to analyze the impact of awareness on SIS epidemic dynamics on various network types, highlighting the epidemic mitigation effects.

Findings

Awareness reduces expected epidemic metrics such as total infections.

Adding awareness can prevent the emergence of endemic states under certain conditions.

Social distancing effects vary across different network structures.

Abstract

We study an SIS epidemic process over a static contact network where the nodes have partial information about the epidemic state. They react by limiting their interactions with their neighbors when they believe the epidemic is currently prevalent. A node's awareness is weighted by the fraction of infected neighbors in their social network, and a global broadcast of the fraction of infected nodes in the entire network. The dynamics of the benchmark (no awareness) and awareness models are described by discrete-time Markov chains, from which mean-field approximations (MFA) are derived. The states of the MFA are interpreted as the nodes' probabilities of being infected. We show a sufficient condition for existence of a "metastable", or endemic, state of the awareness model coincides with that of the benchmark model. Furthermore, we use a coupling technique to give a full stochastic comparison analysis between the two chains, which serves as a probabilistic analogue to the MFA analysis. In particular, we show that adding awareness reduces the expectation of any epidemic metric on the space of sample paths, e.g. eradication time or total infections. We characterize the reduction in expectations in terms of the coupling distribution. In simulations, we evaluate the effect social distancing has on contact networks from different random graph families (geometric, Erd\H{o}s-Renyi, and scale-free random networks).