  The first passage search of a diffusing target (prey) by multiple searchers
(predators) in confinement is an important problem in the stochastic process
literature. While the analogous problem in open space has been studied in some
details, a systematic study in confined space is still lacking. In this paper,
we study the first passage times for this problem in 1,2 and $3-$dimensions.
Due to confinement, the survival probability of the target takes a form $\sim
e^{-t/\tau}$ at large times $t$. The characteristic capture timescale $\tau$
associated with the rare capture events are rather challenging to measure. We
use a computational algorithm that allows us to estimate $\tau$ with high
accuracy. We study in details the behavior of $\tau$ as a function of the
system parameters, namely, the number of searchers $N$, the relative
diffusivity $r$ of the target with respect to the searcher, and the system
size. We find that $\tau$ deviates from the $\sim 1/N$ scaling seen in the case
of a static target, and this deviation varies continuously with $r$ and the
spatial dimensions.
