  Mesh-like structures, such as mucus gel or cytoskeleton networks, are
ubiquitous in biological systems. These intricate structures are composed of
cross-linked, semi-flexible bio-filaments, crucial to numerous biological
processes. In many biological systems, active self-propelled particles like
motor proteins or bacteria navigate these intricate polymer networks. In this
study, we develop a computational model of three-dimensional cubic-topological,
swollen polymer networks of semi-flexible filaments. We perform Langevin
dynamics simulations to investigate the diffusion of active tracer particles
navigating through these networks. By analyzing various physical observables,
we investigate the effects of mesh-to-particle size ratio, P\'eclet number of
active particles, and bending stiffness of the polymer networks upon active
trapped-and-hopping diffusion of the tracer. When the tracer size is equal to
or larger than the mesh size, the polymer stiffness substantially enhances
trapping while suppressing the hopping process. Notably, the mean trapped time
exhibits an exponential growth law to the bending stiffness with an
activity-dependent slope. An analytic theory based on the mean first-passage
time of active particles in a harmonic potential is developed. Our findings
deepen the comprehension of the intricate interplay between the polymer's
bending stiffness, tracer size, and the activity of tracer particles. This
knowledge can shed light on important biological processes, such as
motor-driven cargo transport or drug delivery, which hinge on the behavior of
active particles within biological gels.
