Figure 1.
This figure illustrates the different MOI models. For all panels, the number of infecting virions per cell is on the abscissae, and the frequency thereof is on the ordinate. The black portion of bars is the frequency of single-variant infected cells, whereas the striped portion corresponds to the frequency of mixed-variant infected cells. The white portion of bars in Panels E and F corresponds to cells that are not infected by the virus because they are invulnerable to infection, as a consequence of the aggregation of virus-infected cells. For all left-hand panels, half of the cells are uninfected ( = 0.5), whereas for the right hand panel, only one-fifth of the cells remain uninfected (
= 0.2). For each panel we also report the overall frequency of mixed-variant infections (
), the mean number of infecting virions in infected cells (mI), and model parameters. The frequency of the two virus variants is assumed to be 1∶1 in all cases. Panels A and B illustrate Model 2, the simple Poisson model. Panels C and D illustrate Model 3, which incorporates the effects of spatial segregation of virus variants during expansion, the strength of which is determined by time (t) and a constant Ψ. Note that mI and the overall shape of the distributions are the same; the only difference is the lower frequency of mixed-variant infections for Model 3. Panels E and F illustrate Model 4, which incorporates a fraction of cells β that can become infected, and a fraction 1 − β that cannot. For this model, the zero-term of the Poisson distribution is composed of only those cells can become infected but are in fact uninfected, leading to a higher mI and
. Panels G and H illustrate Model 5, which incorporates super-infection exclusion as determined by time and a parameter μ. This leads to a reduction of both mI and
. For Model 5, we have not illustrated ω, the level of super-infection exclusion at t = 0, which has the same effect as μ but in a time independent manner.
Table 1.
Overview of Models 2 through 9.
Figure 2.
The relationship between mT (abscissae) and mI (ordinate) is plotted as the continuous line. The dotted line is a 1∶1 relationship, given for comparative purposes. mI>mT, although for higher values (>4) the difference becomes very small. Note that mT and has a range [0,∞) whilst mI has a range [1,∞).
Table 2.
Test of the Poisson model.
Table 3.
Model selection with the data of Study 1.
Table 4.
Model selection with the data of Study 2.
Figure 3.
A comparison of mI estimates from Models 1, 2 and 6.
The estimated MOI (mi) is given for the inoculated leaf in Study 1 (Panels A, D and G), for the systemic leaf in Study 1 (Panel B, E and H), and for different systemic leaves collected at different times points in Study 2 (Panel C, F and I) using Model 1 (Panels A–C), Model 2 (Panels D–F), Model 3 (Panels G and H, blue lines and diamonds) and Model 6 (Panel I, red lines and squares). Model 3 is the best-supported model for the Study 1 data, whereas Model 6 is the best-supported model for the Study 2 data. The days post-inoculation (dpi) are given on the abscissae, whereas mI is the ordinates. Error bars represent the 95% CI, and are marked with an asterisk when they extend to infinity (Panel I at 21 dpi). For the data of Study 1 (Panels A, B, D, E, G, and H), Models 1 and 2 both predict that MOI remains low throughout infection. On the other hand, Model 3 predicts that MOI increases over time, as this model incorporates the effects of spatial segregation of variants (Panels G and H). Note that Model 6 predictions are nearly identical to Model 3 predictions for Study 1. For the data of Study 2 (Panels C, F and I), model predictions are roughly similar and the dynamic pattern is the same. However, the differences in MOI over time are less pronounced for Model 6, in particular the decrease of MOI towards the end of infection. This difference is again due to predicted segregation of variants incorporated in Model 6, although the predicted effects thereof are much weaker for the data in Study 2 than in Study 1 (Tables 3 and 4).