# Efficiency of prompt quarantine measures on a susceptible-infected-removed model in networks

## TL;DR

This paper analyzes how prompt quarantine measures can effectively suppress epidemics in network models, demonstrating through simulations and analytical derivations that timely quarantining significantly reduces infection spread, especially in complex networks.

## Contribution

It introduces an analytical framework for the effectiveness of prompt quarantine in SIR models and compares its performance to vaccination strategies in various network types.

## Key findings

- Prompt quarantine outperforms vaccination schemes in reducing infections.
- Analytical epidemic thresholds are derived under quarantine measures.
- Quarantine remains effective even with low detection probabilities in scale-free networks.

## Abstract

This study focuses on investigating the manner in which a prompt quarantine measure suppresses epidemics in networks. A simple and ideal quarantine measure is considered in which an individual is detected with a probability immediately after it becomes infected and the detected one and its neighbors are promptly isolated. The efficiency of this quarantine in suppressing a susceptible-infected-removed (SIR) model is tested in random graphs and uncorrelated scale-free networks. Monte Carlo simulations are used to show that the prompt quarantine measure outperforms random and acquaintance preventive vaccination schemes in terms of reducing the number of infected individuals. The epidemic threshold for the SIR model is analytically derived under the quarantine measure, and the theoretical findings indicate that prompt executions of quarantines are highly effective in containing epidemics. Even if infected individuals are detected with a very low probability, the SIR model under a prompt quarantine measure has finite epidemic thresholds in fat-tailed scale-free networks in which an infected individual can always cause an outbreak of a finite relative size without any measure. The numerical simulations also demonstrate that the present quarantine measure is effective in suppressing epidemics in real networks.