If disease progress in monocyclic epidemics is linear, the slope of the disease progress curve is constant. Furthermore, if disease progress in a monocyclic epidemic is proportional to the amount of initial inoculum (which is itself constant during the epidemic), we can make the slope of the disease progress curve the product of initial inoculum and a proportionality constant. Therefore, we can describe a monocyclic epidemic with linear disease progress using the differential equation:

where is an infinitesimally small increment in the proportion of disease, is an infinitesimally small time step, is the amount of initial inoculum, and is a proportionality constant that represents the rate of disease progress per unit of inoculum. Since and are both constant during the course of an epidemic, the slope, , is constant, and disease progress is linear. Just as with the constant in the model of monocyclic inoculum production, has a value that represents the "average" for the whole epidemic, a value that depends upon many factors, such as aggressiveness of pathogen, susceptibility of the host, the environmental conditions, etc. The units of are proportion per unit initial inoculum per unit time.

If we integrate the above differential equation, we get:

Graphically we see a straight line with an intercept of zero and a slope of