  Consider a uniformly mixing population which grows as a super-critical linear
birth and death process. At some time an infectious disease (of SIR or SEIR
type) is introduced by one individual being infected from outside. It is shown
that three different scenarios may occur: 1) an epidemic never takes off, 2) an
epidemic gets going and grows but at a slower rate than the community thus
still being negligible in terms of population fractions, or 3) an epidemic
takes off and grows quicker than the community eventually leading to an endemic
equilibrium. Depending on the parameter values, either scenario 1 is the only
possibility, both scenario 1 and 2 are possible, or scenario 1 and 3 are
possible.
