  The discovery of fast radio bursts (FRBs) about a decade ago opened up new
possibilities for probing the ionization history of the Intergalactic Medium
(IGM). In this paper we study the use of FRBs for tracing the epoch of HeII
reionization, using simulations of their dispersion measures. We model
dispersion measure contributions from the Milky Way, the IGM (homogeneous and
inhomogeneous) and a possible host galaxy as a function of redshift and star
formation rate. We estimate the number of FRBs required to distinguish between
a model of the Universe in which helium reionization occurred at z = 3 from a
model in which it occurred at z = 6 using a 2-sample Kolmogorov-Smirnoff test.
We find that if the IGM is homogeneous >1100 FRBs are needed and that an
inhomogeneous model in which traversal of the FRB pulse through galaxy halos
increases the number of FRBs modestly, to >1600. We also find that to
distinguish between a reionization that occurred at z = 3 or z = 3.5 requires
~5700 FRBs in the range 3 < z < 5.
