  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.
