Key steps, decision points and probabilities of the 3 D stochastic model. The following parameters were used to determine cell death and replacement, and infection. Cells that do, or do not, contain the integrated gene are referred to as transduced (Tx) or untransduced (UNTx) respectively. Tx or UNTx cells can either be uninfected or infected. (A) The replacement of an infected cell is determined by (1) finding the infected UNTx or Tx cells, (2) identifying the infected dead cells, and (3) replacing them with cells divided from uninfected neighbours or newly matured from the thymus (B) Infection is established by (4) finding an uninfected cell with at least one infected neighbour and determining the protection of the uninfected cell, i.e. is it UNTx or Tx (and with how many shRNAs)? (5) The status of the infected neighbour is used to determine the likely number of virions produced and their sequence. (6) The virion sequence is mutated and recombined as necessary. (7) Cells are infected depending on the infecting viral sequence, any inhibitory shRNA, and chance. (8) The life span of the newly infected cell is randomly assigned and the viral fitness is adjusted according to its mutations/recombinations. Probabilities: P.tx (set at either 0.2 or 0.01): the percentage of Tx CD34+ hematopoietic stem cells (HSC) resulting in this percentage of cells exported from thymus containing gene product. P.neigh (set at 0.99): the replacement by an uninfected neighbour, compared to a cell from the thymus. P.mut (set at 3.4 × 10-5): the mutation rate per nucleotide. Viral productivity: determined by viral fitness, the transduction state of the infected cell (Tx or UNTx) and the number of mutated sequences. Life span: Poisson distributed with mean 2 days, measured in 12-hourly intervals. P.long (set at 0.0183): probability that an infected cell is long lived.