Parameter estimation and saddlepoint distributions for models in plant disease epidemics.

摘要

There are numerous models, both deterministic and stochastic, available in plant disease literature. Most of these models consider the growth of the epidemic as a function solely of the amounts (or proportions) of susceptible and/or infective tissue and do not take into account other factors that may play a role in the infection process. For example, there is no provision for a latent period, ;Secondly, methods for estimating the infection rate parameter for the generalized Gompertz model and the generalized Richards model are derived by using Taylor series expansion and regression-type techniques. These methods are illustrated by obtaining estimates for the infection rate using data on the spread of the disease anthracnose in the plant Stylosanthes scabra. A comparison between the two models is made.;Next, we look at a stochastic model where the amount of leaf infection and the amount of stem infection are treated as two distinct random variables. Stem infection can play a significant role in the spread of disease and hence is considered as a separate entity in this model. Thus, we have a pure bivariate birth process. An important measure of disease spread is considered to be the area under the disease progress curve, also known as plant stress. In this dissertation, we have obtained the asymptotic distribution of plant stress by using the method of saddlepoint approximation. Two cases are considered separately: one, when the stem is initially uninfected and second, when the stem is initially infected. The mean and the variance of stress is calculated for different values of the parameters. Comparisons are made between the renormalized saddlepoint distribution and the normal distribution.