# Consequences of delays and imperfect implementation of isolation in epidemic control

## TL;DR

This paper introduces an epidemic model analyzing how delays and imperfect isolation impact outbreak control, providing insights into response capabilities needed to prevent endemic states.

## Contribution

It presents a novel SIQ model with delay differential equations to quantify the effects of isolation delays and incomplete detection on epidemic outcomes.

## Key findings

- Isolation effectiveness depends on speed of identification and isolation probability.
- Minimum response capabilities can be estimated to prevent endemic states.
- Model provides explicit parameters for evaluating epidemic preparedness.

## Abstract

For centuries isolation has been the main control strategy of unforeseen epidemic outbreaks. When implemented in full and without delay, isolation is very effective. However, flawless implementation is seldom feasible in practice. We present an epidemic model called SIQ with an isolation protocol, focusing on the consequences of delays and incomplete identification of infected hosts. The continuum limit of this model is a system of Delay Differential Equations, the analysis of which reveals clearly the dependence of epidemic evolution on model parameters including disease reproductive number, isolation probability, speed of identification of infected hosts and recovery rates. Our model offers estimates on minimum response capabilities needed to curb outbreaks,and predictions of endemic states when containment fails. Critical response capability is expressed explicitly in terms of parameters that are easy to obtain, to assist in the evaluation of funding priorities involving preparedness and epidemics management.