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
A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in the natural sciences (such as physics, ...
is fit. The model is based upon two assumptions:
* the progress of the infection is constrained by the amount of tissue that remains to be infected; and
* if it were not so constrained, the extent of infection would exhibit
exponential growth
Exponential growth is a process that increases quantity over time. It occurs when the instantaneous rate of change (that is, the derivative) of a quantity with respect to time is proportional to the quantity itself. Described as a function, a q ...
.
There is a single model parameter ''r'', which is the apparent infection rate. It can be calculated analytically using the formula
: