  Active cellular transport is a fundamental mechanism for protein and vesicle
delivery, cell cycle and molecular degradation. Viruses can hijack the
transport system and use it to reach the nucleus. Most transport processes
consist of intermittent dynamics, where the motion of a particle, such as a
virus, alternates between pure Brownian and directed movement along
microtubules. In this communication, we estimate the mean time for particle to
attach to a microtubule network. This computation leads to a coarse grained
equation of the intermittent motion in radial and cylindrical geometries.
Finally, by using the degradation activity inside the cytoplasm, we obtain
refined asymptotic estimations for the probability and the mean time a virus
reaches a small nuclear pore.
