  We are studying the effect of converting caught targets into new chasers in
the context of the recently proposed `group chase and escape' problem.
Numerical simulations have shown that this conversion can substantially reduce
the lifetimes of the targets when a large number of them are initially present.
At the same time, it also leads to a non-monotonic dependence on the initial
number of targets, resulting in the existence of a maximum lifetime. As a
counter effect for this conversion, we further introduce self-multiplying
abilities to the targets. We found that the longest lifetime exists when
suitable combination of these two effects is created.
