Master equation solution of a plant disease model

We develop the exact solution for a stochastic plant disease model with non linear density dependence and time-decaying susceptibility. In our biologic al application only the transient behaviour, rather than the stationary sta te, is relevant. To model the population noise we use the Master equation, lending to a linear ordinary differential equation system with finally time -independent coefficients. A numerically stable procedure is given by the P ade approximation of the solution in form of an exponential of a matrix. On the basis of this solution the parameter estimation is performed using exp erimental data from epidemiological microcosms. In the Master equation formalism, in order to generalize to more complicate d models, for example, including a time-independent latent period as a firs t multivariate model, we finally suggest a numerical procedure to estimate the likelihood comparing data time series with simulated Master equation ti me series. (C) 2000 Published by Elsevier Science B.V.