  We study the epicyclic oscillatory motion around circular orbits of the
traversable asymptotically flat and reflection-symmetric wormholes obtained in
the Einstein-Dirac-Maxwell theory without applying exotic matter in their
construction. We determine frequencies of the orbital and epicyclic motion in
the Keplerian disks having inner edge at the marginally stable circular
geodesic of the spacetime. The obtained frequencies are applied in the so
called geodesic models of high-frequency quasiperiodic oscillations (HF QPOs)
observed in microquasars and active galactic nuclei containing a supermassive
central object. We show that even the simplest epicyclic resonance variant of
the geodesic models can explain the HF QPOs observed in many active galactic
nuclei for realistic choices of the wormhole parameters, but there are some of
the sources where only wormholes with unrealistically large values of the
parameters can be sufficient for the explanation. On the other hand, in the
case of microquasars, the observed HF QPOs strongly restrict the acceptable
values of the wormhole parameters.
