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2014 Stability and Sensitivity Analysis of a Plant Disease Model with Continuous Cultural Control Strategy
Zhang Zhonghua, Suo Yaohong
J. Appl. Math. 2014: 1-15 (2014). DOI: 10.1155/2014/207959

Abstract

In this paper, a plant disease model with continuous cultural control strategy and time delay is formulated. Then, how the time delay affects the overall disease progression and, mathematically, how the delay affects the dynamics of the model are investigated. By analyzing the transendental characteristic equation, stability conditions related to the time delay are derived for the disease-free equilibrium. Specially, when R0=1, the Jacobi matrix of the model at the disease-free equilibrium always has a simple zero eigenvalue for all τ0. The center manifold reduction and the normal form theory are used to discuss the stability and the steady-state bifurcations of the model near the nonhyperbolic disease-free equilibrium. Then, the sensitivity analysis of the threshold parameter R0 and the positive equilibrium E* is carried out in order to determine the relative importance of different factors responsible for disease transmission. Finally, numerical simulations are employed to support the qualitative results.

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Zhang Zhonghua. Suo Yaohong. "Stability and Sensitivity Analysis of a Plant Disease Model with Continuous Cultural Control Strategy." J. Appl. Math. 2014 1 - 15, 2014. https://doi.org/10.1155/2014/207959

Information

Published: 2014
First available in Project Euclid: 2 March 2015

zbMATH: 07010570
Digital Object Identifier: 10.1155/2014/207959

Rights: Copyright © 2014 Hindawi

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