  In this work, after making an attempt to improve the formulation of the model
on particle transport within astrophysical plasma outflows and constructing the
appropriate algorithms, we test the reliability and effectiveness of our method
through numerical simulations on well-studied Galactic microquasars as the SS
433 and the Cyg X-1 systems. Then, we concentrate on predictions of the
associated emissions, focusing on detectable high energy neutrinos and
$\gamma$-rays originated from the extra-galactic M33 X-7 system, which is a
recently discovered X-ray binary located in the neighboring galaxy Messier 33
and has not yet been modeled in detail. The particle and radiation energy
distributions, produced from magnetized astrophysical jets in the context of
our method, are assumed to originate from decay and scattering processes taking
place among the secondary particles created when hot (relativistic) protons of
the jet scatter on thermal (cold) ones (p-p interaction mechanism inside the
jet). These distributions are computed by solving the system of coupled
integro-differential transport equations of multi-particle processes (reactions
chain) following the inelastic proton-proton (p-p) collisions. For the
detection of such high energy neutrinos as well as multi-wavelength (radio,
X-ray and gamma-ray) emissions, extremely sensitive detection instruments are
in operation or have been designed like the CTA, IceCube, ANTARES, KM3NeT,
IceCube-Gen-2, and other space telescopes.
