Example 1: Suppose that in the flax wilt example we surveyed an adjacent field and found a level of initial inoculum that was 1% of that in the field showing severe wilt symptoms. What incidence of infection would we expect in this field at the end of the season (60 days)? To simplify the calculations, let us assume that the final incidence will be so low that we can ignore the correction for healthy plants remaining and use the simple linear model. In our example we averaged of 57 colony-forming units per gram of soil, so 1% of that would be 0.57 CFU. We calculated R to be 0.0013/CFU/Day, and therefore the proportion of plants infected after 60 days would be:
x = QRt = (0.57)(0.0013)(60)
= 0.044 or about 4%
Example 2: Suppose that in the halo blight example we wanted to estimate what incidence of seed infection would be the maximum tolerable to keep the final incidence of disease below 25%. We will assume a 90-day season, and again because the final incidence is low, we will ignore the logistic correction and use the simple exponential model:
Substituting 0.25 for x, our estimated 0.124/Day for r, and 90 Days for t, we get:
0.25 = x0 exp((0.124)(90))
0.25 = x0 exp(11.16)
x0 = 0.25/70263 = 0.0000036
This calculates to an initial disease incidence of about one plant in 280,000.