The above models assume unlimited growth of disease, which, of course, is impossible; the proportion of diseased plants or of diseased tissue cannot exceed one. We can adjust our models to address this issue by using a correction factor to represent the proportion of healthy tissue remaining. A decrease in the remaining healthy tissue reduces the chance for new infections and therefore reduces the rate of disease progress. As approaches one, there is no healthy tissue left, and the rate of the epidemic slows to zero.

The monocyclic model of disease progress, adjusted for the limit to disease is:

Graphically we see an epidemic that starts out looking linear, but as approaches 1, the slope decreases to zero.

In the polycyclic model we make a similar adjustment:

     

This model starts out approximately exponential, but its slope also decreases and approaches zero as increases and approaches one. The result is a sigmoid-shaped curve:

In reality, it is rare that disease incidence or severity exceeds 50%, and when it does, the disease progress curve is usually not quite sigmoid. For a discussion of other models of disease progress, see Neher and Campbell, 1992 and Gilligan, 2002.