Epidemic control in networks with cliques

TL;DR

This paper investigates how quarantine strategies in networks with social units like households can abruptly suppress epidemics, revealing complex phase transition behaviors including both discontinuous and continuous transitions.

Contribution

It introduces an epidemic model with prompt quarantine on networks with cliques, analyzing phase transitions and bifurcations both numerically and analytically.

Findings

Epidemic outbreaks are abruptly suppressed at a critical quarantine probability.

Small outbreaks exhibit second-order phase transition features around the critical point.

The model shows a backward bifurcation phenomenon.

Abstract

Social units, such as households and schools, can play an important role in controlling epidemic outbreaks. In this work, we study an epidemic model with a prompt quarantine measure on networks with cliques (a $clique$ is a fully connected subgraph representing a social unit). According to this strategy, newly infected individuals are detected and quarantined (along with their close contacts) with probability $f$. Numerical simulations reveal that epidemic outbreaks in networks with cliques are abruptly suppressed at a transition point $f_c$. However, small outbreaks show features of a second-order phase transition around $f_c$. Therefore, our model can exhibit properties of both discontinuous and continuous phase transitions. Next, we show analytically that the probability of small outbreaks goes continuously to 1 at $f_c$ in the thermodynamic limit. Finally, we find that our model exhibits a backward bifurcation phenomenon.