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A continuous time Markov chain model for a plantation-nursery system

✍ Scribed by J. Gani; L. Stals

Publisher: John Wiley and Sons
Year: 2005
Tongue: English
Weight: 157 KB
Volume: 16
Category: Article
ISSN: 1180-4009
DOI: 10.1002/env.740

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✦ Synopsis

Abstract

This article examines a continuous time Markov chain model for a plantation‐nursery system in which diseased plantation trees are replaced at a daily rate λ by nursery seedlings. There is a random infection rate α caused by insects, and the disease is also spread directly between the N plantation trees at the rate β, starting with a diseased trees at time t = 0; in addition, some replacement seedlings prove to be infected with probability 0 < p. < 1. We find a formal solution to the system in terms of the Laplace transforms $\hat p_j$, j = 0,…, N, of the probabilities p~j~(t) of j infected plantation trees at time t. A very simple example for N = 2, a = 1 is used to illustrate the method. We then consider numerically the effect of the parameters λ, α, and β on the system, and for small t study the influence of the initial number a of infected trees on the expected number of such trees at time t ≤ 365. As t → ∞, stationarity is achieved, irrespective of the initial value a. Copyright © 2005 John Wiley & Sons, Ltd.

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