  An impulsive model of augmentative biological control consisting of a general
continuous predator-prey model in ordinary differential equations augmented by
a discrete part describing periodic introductions of predators is considered.
It is shown that there exists an invariant periodic solution that corresponds
to prey eradication and a condition ensuring its global asymptotic stability is
given. An optimisation problem related to the preemptive use of augmentative
biological control is then considered. It is assumed that the per time unit
budget of biological control (i.e. the number of predators to be released) is
fixed and the best deployment of this budget is sought after in terms of
release frequency. The cost function to be minimised is the time taken to
reduce an unforeseen prey (pest) invasion under some harmless level. The
analysis shows that the optimisation problem admits a countable infinite number
of solutions. An argumentation considering the required robustness of the
optimisation result is then conducted and it is shown that the best deployment
is to use as frequent (and thus as small) as possible predator introductions.
