  This paper is concerned with Crump-Mode-Jagers branching processes,
describing spread of an epidemic depending on the proportion of the population
that is vaccinated. Births in the branching process are aborted independently
with a time-dependent probability given by the fraction of the population
vaccinated. Stochastic monotonicity and continuity results for a wide class of
functions (e.g., extinction time and total number of births over all time)
defined on such a branching process are proved using coupling arguments,
leading to optimal vaccination schemes to control corresponding functions
(e.g., duration and final size) of epidemic outbreaks. The theory is
illustrated by applications to the control of the duration of mumps outbreaks
in Bulgaria.
