Before revision:  We present here a general approach to estimate the probability and the conditional mean first passage time for such a viral particle to attain safely the nucleus, covered with many (around two thousands ) small absorbing pores. Due to this large number of small holes, which defines the limiting scale , any Brownian simulationsare very unstable. Our new asymptotic formulas precisely account for this phenomena and allow to quantify the cytoplasmic stage of viral infection .
After revision:  We present here a general approach to estimate the probability and the conditional mean first passage time for such a viral particle to attain alive the nucleus. The cell nucleus is covered with thousands of small absorbing nuclear pores and the minimum distance between them defines the smallest spatial scale that limits the efficiency of stochastic simulations. Using the Neuman-Green's function method to solve the steady-state Fokker-Planck equation, we derive asymptotic formula for the probability and mean arrival time to a small window for various pores' distributions, that agree with stochastic simulations. These formulas reveal how key geometrical parameters defines the cytoplasmic stage of viral infection .