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

Consequences of delays and imperfect implementation of isolation in epidemic control