In a model analogous to that of polycyclic inoculum production, the rate of change in disease is proportional to amount of disease at any point in time. Therefore, in differential form, the equation to describe polycyclic epidemics is:

As with the monocyclic model, is a dimensionless proportion between zero and one, and is a constant that depends on the aggressiveness of pathogen, the susceptibility of the host, the environmental conditions, etc., averaged over the course of the epidemic. In this case, the slope, , is proportional to , and therefore disease progress increases with time at an increasing rate.

In the integrated form the model is:

where is the proportion of disease at the start of the epidemic and is the base of the natural logarithm. Vanderplank (1963) called the "apparent infection rate" because it is based on the appearance of disease symptoms, which lag behind the actual infections. It is defined as the rate of disease increase per unit of disease and has the units of proportion per unit of time. The parameter is sometimes carelessly called initial inoculum, to which it is quantitatively related, but strictly speaking it is the initial disease (a proportion). Graphically the model has the familiar form of the exponential model: