Superexponential growth of epidemics in networks with cliques

TL;DR

This paper studies how epidemics can grow superexponentially in networks with cliques, revealing a critical threshold for rapid outbreak escalation and emphasizing the importance of network structure in disease dynamics.

Contribution

It introduces a susceptible-infected-quarantined (SIQ) model on clique networks, deriving equations and identifying a critical threshold where epidemic growth accelerates dramatically.

Findings

Final infected proportion shows a sudden transition at a critical testing access threshold.

Near the threshold, epidemic growth can be faster than exponential.

Larger cliques increase the likelihood of superexponential epidemic spread.

Abstract

Many dynamic processes on complex networks, from disease outbreaks to cascading failures, can rapidly accelerate once a critical threshold is exceeded, potentially leading to severe social and economic costs. Therefore, in order to develop effective mitigation strategies, it is essential to understand how these catastrophic events occur. In this work, we investigate the dynamic of disease propagation on networks with fully connected sub-graphs (or cliques) using a susceptible-infected-quarantined (SIQ) model, and considering a scenario where only a proportion $f$ of the population has access to testing. For this model, we derive the time-evolution equations governing the spread of epidemics and show that the final proportion of infected individuals undergoes a sudden transition at a critical threshold $f_c$. Moreover, close to this transition point, our results on the time evolution of the SIQ model reveal that the number of new cases can exhibit a faster-than-exponential growth. This accelerated spread dynamics is more likely to occur in networks with larger cliques.