Assessment of plant stress due to the presence of disease

One of the concerns of a plant scientist is the need to control disease and its spread through crops, plants, and pasture. This leads to the study of the progress of disease as it spreads through the plant and, in particular, to plant stress measured by the area under the disease progress curve. A n ice review of this and related concepts has been provided elsewhere, but th at work restricts attention to deterministic models. In this work, we devel op a stochastic model for disease spread. Hence, plant stress is a stochast ic variable. We show that this stress follows a mixture distribution relate d to sums of known exponential random variables, and we derive the correspo nding mean and variance of stress experienced by the plant until prespecifi ed proportions become infected. Through numerical illustrations, we discuss the significance of the model parameters. We also derive limiting formulas as the number of leaves/size of plants becomes large.