To apply our models to real epidemics, we would like to come up with numerical values for their parameters ( in the monocyclic model and and in the polycyclic model). To estimate the parameters, we observe the epidemic, measure at several times during the epidemic, and then plot versus . The difficulty comes in trying to fit nonlinear models to the data sets. It is far easier to transform the x's to get a linear model that can be fit with simple linear regression.

The monocyclic model

In the case of the monocyclic model, if the observed x's are transformed to the natural logarithm of 1/(1-x), and these transformed values are plotted against t, we will get a straight line with a slope equal to QR.

Then with an independent estimate of the initial inoculum, Q, we can calculate R.

The polycyclic model

If the observed x's in a polycyclic epidemic are transformed to the natural logarithm of x/(1-x), and the transformed values are plotted against t, the result will be a straight line with a slope equal to r and an intercept equal to the natural log of x₀/(1-x₀).

In fitting models to observed data, it is important to select the model based on the known biology of the pathogen rather than simply on the shape of the curve. Likewise, one must not attempt to make inferences about the biology of the pathogen based on the shape of the curve and which model gives the "best fit" of the data. There is random variability in each observation, and in the transformed models the data points on the ends of the line have undue weight in determining the fit to the model. It is quite possible to have a data set that fits both the monocyclic and polycyclic models equally well or to have a data set from a known monocyclic epidemic that gives a better fit to a polycyclic model and vice versa.