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 nice review of this and related concepts has been provided elsewhere, but that work restricts attention to deterministic models. In this work, we develop a stochastic model for disease spread. Hence, plant stress is a stochastic variable. We show that this stress follows a mixture distribution related to sums of known exponential random variables, and we derive the corresponding mean and variance of stress experienced by the plant until prespecified 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.