Probabilistic model of IVG costs for population infectivity

To define the impact of incomplete viral genomes on the ability of a virus population to establish infection in a population of cells, the probabilistic model described above was adapted to account for the Poisson distribution of virions among a population of cells. It is assumed that one productively infected cell produces enough virions to infect other cells in subsequent rounds of replication, and so establishing infection in a population of cells requires that at least one cell receive all 8 genome segments. For a given MOI, the probability of a cell being infected by v virions follows the Poisson distribution

At each v, the probability that a cell received any given segment is equal to 1 – (1 – P_P)^v, and so the probability that a cell is productively infected after infection with v virions is

The sum of the joint probabilities pv*p(8∣v) across all values of v gives the probability that any given cell is productively infected:

Multiplying this probability by the number of cells in the population gives the expected number of cells infected, and the probability of the population becoming infected is equal to this value or 1, whichever is lower. The ID₅₀ was estimated as the lowest MOI yielding a probability ≥ 50%. A similar analysis was used to estimate the ID₅₀ when complementation was not allowed, with the p(8|v) function being modified to

to reflect the fact that only complete viral genomes could initiate infection. Finally, the percentage of infected cells that contained incomplete viral genomes was calculated by estimating the probability that a cell infected by v virions contained between one and seven segments,

and determining the total proportion of infected cells containing IVGs using the equation