  The energy evolution of medium-modified average multiplicities and
multiplicity fluctuations in quark and gluon jets produced in heavy-ion
collisions is investigated from a toy QCD-inspired model. In this model, we use
modified splitting functions accounting for medium-enhanced radiation of gluons
by a fast parton which propagates through the quark gluon plasma. The leading
contribution of the standard production of soft hadrons is found to be enhanced
by the factor $\sqrt{N_s}$ while next-to-leading order (NLO) corrections are
suppressed by $1/\sqrt{N_s}$, where the nuclear parameter $N_s>1$ accounts for
the induced-soft gluons in the hot medium. The role of next-to-next-to-leading
order corrections (NNLO) is studied and the large amount of medium-induced soft
gluons is found to drastically affect the convergence of the perturbative
series. Our results for such global observables are cross-checked and compared
with their limits in the vacuum and a new method for solving the second
multiplicity correlator evolution equations is proposed.
