Table 1.
Description of model parameters and units (if applicable).
Table 2.
Approximate average run times for a single simulation for the completely deterministic ODE system (Euler method with step-size h = 10−5), the hybrid method with different threshold values (), and the completely stochastic Gillespie algorithm (rows). Each system is run for the single mutation, double mutation, and triple mutation models (columns). In each system we assume all strains are neutral (Fi = 1 for all i). The other parameters are N = 3, μ = 3 × 10−5, λ = 1.59 × 107, β = 3.60 × 10−9, γ = 0, d = 0.016, and a = 0.45.
Fig 1.
Comparison of the deterministic prediction and stochastic average of the number of cells infected with the mutant with free virus transmission only.
The deterministic predictions are in blue and the stochastic hybrid simulations with (infected populations always treated completely stochastically) are in yellow. Standard error bars are included in the main panel (sometimes too small to see) and the inserts show standard deviation bars. A Neutral mutant, Fmutant = 0.9. Each yellow dot represents the average taken over at least 2 × 106 simulations. B Advantageous mutant with 10% advantage, Fmutant = 0.99. Each yellow dot represents the average taken over at least 1.1 × 103 simulations. C Disadvantageous mutant with 10% disadvantage, Fmutant = 0.81. Each yellow dot represents the average taken over at least 3.5 × 106 simulations. We have
, and the parameters are Fwild-type = 0.9, N = 3, μ = 3 × 10−5, λ = 1.59 × 107, β = 4 × 10−9, γ = 0, and d = 0.016. The infected cell death rate a is adjusted to achieve the required R0.
Fig 2.
Neutral mutant evolution in the absence of synaptic transmission, comparing simulations with single infection only (N = 1, blue) and in the presence of multiple infection (N = 11, red).
The mean values are shown by the vertical lines (blue for single infection only and red for multiple infection). For both panels, the Kolmogorov-Smirnov test between the two cases gives a p-value less than 10−6. A Number of cells infected with one of the single mutant strains. The average for single infection is approximately 3.7 × 105 and for multiple infection is approximately 7.6 × 105. B Number of cells infected with the double mutant strain. The average for single infection is approximately 271 and for multiple infection is approximately 551. Histograms represent 4 × 103 hybrid simulations with size threshold . Simulations in which infections are not established (or in the rare case a simulation does not reach the infected size threshold) are discarded. Simulations are stopped when the infected cell population is close to peak infection (6 × 108 cells). The other parameters are similar to Fig 1 (Fwild-type = 1, Fmutant = 1, μ = 3 × 10−5, λ = 1.59 × 107, β = 3.60 × 10−9, γ = 0, a = 0.45, d = 0.016, and R0 = 8).
Fig 3.
Zero fitness mutants, comparing the effect of complementation for free virus and synaptic transmission.
All simulations start with a single infected cell coinfected with a single copy of both the wild-type and mutant, and mutation is turned off (μ = 0). A Only free virus transmission (β = 3.60 × 10−9, γ = 0, N = 11) with complementation. The average number (standard deviation) of cells infected with the mutant is 0.71 (1.73). B Only synaptic transmission (β = 0, γ = 3.60 × 10−9, N = 25, see Section 1.3 of S1 Text for justification) with complementation. The average number (standard deviation) of cells infected with the mutant is 3.1 × 105 (2.2 × 105). Histograms represent 5 × 103 hybrid simulations with size threshold . Simulations in which infections are not established (or in the rare case a simulation does not reach the infected size threshold) are discarded; simulations are stopped when the infected cell population is close to peak infection (5 × 108 cells). The fitness of the wild-type is fixed at Fwild-type = 0.9 and Fmutant = 0. The other parameters are as in Fig 1 (λ = 1.59 × 107, a = 0.45, and d = 0.016).
Fig 4.
Mutant evolution under different scenarios with 100% free virus transmission (left panels: β = 3.6 × 10−9, γ = 0, N = 11) or 100% synaptic transmission (right panels: β = 0, γ = 3.6 × 10−9, S = 3, N = 25).
Panels A and B record the number of cells infected with the mutant at 104 infected cells, for all other panels it is 5 × 108 infected cells. For all panels, the blue bars represents simulations without complementation/interference and the red bars represents simulations with complementation/interference. The mean values are presented in each panel. For panels B-H, p < 10−6 by the Kolmogorov-Smirnov test. A-D Zero fitness mutant (Fmutant = 0). E-F Disadvantageous mutant (Fmutant = 0.81). G-H Advantageous mutant (Fmutant = 0.99). For all simulations, we fix and the other parameters are as in Fig 1 (μ = 3 × 10−5, λ = 1.59 × 107, a = 0.45, and d = 0.016).