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A certain class of viruses replicates inside a cell if they can enter thenucleus through one of many small target pores, before being permanentlytrapped or degraded. We adopt for viral motion a switching stochastic processmodel and we estimate here the probability and the conditional mean firstpassage time for a viral particle to attain alive the nucleus. The cell nucleusis covered with thousands of small absorbing nuclear pores and the minimumdistance between them defines the smallest spatial scale that limits theefficiency of stochastic simulations. Using the Neuman-Green's function methodto solve the steady-state Fokker-Planck equation, we derive asymptotic formulafor the probability and mean arrival time to a small window for various pores'distributions, that agree with stochastic simulations. These formulas revealhow key geometrical parameters defines the cytoplasmic stage of viralinfection.

Narrow escape to small windows on a small ball modeling the viral entry into the cell nucleus