In monocyclic epidemics we are interested primarily in the inoculum present at the beginning of each season (initial inoculum). If we let represent the quantity of initial inoculum at the beginning of the current season, it will be equal to the quantity of initial inoculum at the beginning of the previous season, , plus the increment that has resulted from the pathogen's growth and development during the season:

The increment will be a function of the quantity of last season's initial inoculum, and a reasonable approximation is to make it a simple proportion of last season's initial inoculum, , where is a proportionality constant:

Embodied in are all the factors affecting survival and growth of the fungus, propagule production, dispersal of inoculum, and death of the fungus. The value of depends on a large number of factors, including environmental conditions, crop development, and cultural practices. If there is a net increase in the inoculum from one season to the next, will be positive. If, on the other hand, there is a net loss of inoculum, such as might occur during a rotation to a nonhost crop, would be negative.

In order to describe the changes in the initial inoculum from one season to the next in a polyetic epidemic, we will generalize the subscript that indicates the season.

We solve this equation repetitively, changing the subscript , indicating time, with each successive season and making the current value of the value of in the subsequent season. In order to simplify the equation, we assume a constant (an average over many seasons). The above equation gives the following graph:

Note that if is positive, the increment (the light grey area on each bar) increases with the initial inoculum in each successive season, and the graph appears to curve upward.