  A virus infection can be initiated with very few or even a single infectious
virion, and as such can become extinct, i.e. stochastically fail to take hold
or spread significantly. There are many ways that a fully competent infectious
virion, having successfully entered a cell, can fail to cause a productive
infection, i.e. one that yields infectious virus progeny. Though many discrete,
stochastic mathematical models (DSMs) have been developed and used to estimate
a virus infection's extinction probability, these typically neglect infection
failure post viral entry. The DSM presented herein introduces parameter
$\gamma\in(0,1]$ which corresponds to the probability that a virion's entry
into a cell will result in a productive cell infection. We derive an expression
for the likelihood of infection extinction in this new DSM, and find that
prophylactic therapy with an antiviral acting to reduce $\gamma$ is best at
increasing an infection's extinction probability, compared to antivirals acting
on the rates of virus production or virus entry into cells. Using the DSM, we
investigate the difference in the fraction of cells consumed by so-called
extinct versus established virus infections, and find that this distinction
becomes biologically meaningless as the probability of extinction approaches
100%. We show that infections wherein virus is release by an infected cell as a
single burst, rather than at a constant rate over the cell's infectious
lifespan, has the same probability of infection extinction, despite previous
claims to this effect [Pearson 2011, doi:10.1371/journal.pcbi.1001058].
Instead, extending previous work by others [Yan 2016,
doi:10.1007/s00285-015-0961-5], we show how the assumed distribution for the
stochastic virus burst size, affects the extinction probability and associated
critical antiviral efficacy.
