SIQ: a delay differential equations model for disease control via isolation

TL;DR

This paper introduces a delay differential equations model to analyze the effectiveness of isolation strategies in controlling infectious diseases, providing insights into the minimum response needed to prevent outbreaks and predicting endemic states.

Contribution

It develops a novel delay differential equations model for disease control via isolation and analyzes its dynamics using geometric theory of semi-flows.

Findings

Identifies the minimum response needed to prevent outbreaks.

Predicts endemic states if the infection persists.

Provides a mathematical framework for evaluating isolation strategies.

Abstract

Infectious diseases are among the most prominent threats to mankind. When preventive health care cannot be provided, a viable means of disease control is the isolation of individuals, who may be infected. To study the impact of isolation, we propose a system of Delay Differential Equations and offer our model analysis based on the geometric theory of semi-flows. Calibrating the response to an outbreak in terms of the fraction of infectious individuals isolated and the speed with which this is done, we deduce the minimum response required to curb an incipient outbreak, and predict the ensuing endemic state should the infection continue to spread.