  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.
