How likely is to develop an infection from a single virion entering a single cell?
This is a great biological question! It asks a lot about how empirical science is done in the field of modern biology! I'm glad we encourage such questions from curious people who want to learn more.



This is called the Independent Action Hypothesis, described here:


  The Independent Action Hypothesis (IAH) states that pathogenic individuals (cells, spores, virus particles etc.) behave independently of each other, so that each has an independent probability of causing systemic infection or death.


Zwart et al. (2009) tests this theory, and their results support the hypothesis that a single virus particle can infect a cell:


  The ‘independent action hypothesis’ (IAH) states that each pathogen individual has a non-zero probability of causing host death and that pathogen individuals act independently. IAH has not been rigorously tested. In this paper, we (i) develop a probabilistic framework for testing IAH and (ii) demonstrate that, in two out of the six virus–insect pathosystems tested, IAH is supported by the data.


The modeling done in this paper may be worth reviewing.