Relation Between Rate Parameters and Latent and Infectious Periods During a Plant Disease Epidemic

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Abstract
The observations that epidemic progress is often adequately described by a rate parameter (r) and initial amount of disease (yo), and that calculated values of Vanderplank''s R decrease during an epidemic, are used to obtain explicit time-dependent relationships between r and R during entire epidemics. Analysis of these relationships indicates that R can be calculated from epidemic data only during a finite period of time and that there are constraints on the combination of parameter values possible in such epidemics. Further theoretical threshold results for epidemics are obtained and related to the doubling time, an important parameter in population ecology, of the epidemic. Vanderplank''s R cannot easily be estimated for epidemics in which r is not approximately constant.

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