Apparent infection rate

Apparent infection rate is an estimate of the rate of progress of a disease, based on proportional measures of the extent of infection at different times.
Firstly, a proportional measure of the extent of infection is chosen as the disease extent metric. For example, the metric might be the proportion of leaf area affected by mildew, or the proportion of plants in a population showing dieback lesions. Measures of disease extent are then taken over time, and a mathematical model is fit. The model is based upon two assumptions:
There is a single model parameter "r", which is the apparent infection rate. It can be calculated analytically using the formula
where