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Journal of Applied Mathematics
Volume 2013, Article ID 184054, 10 pages
Research Article

Analysis of the Mathematical Model for the Spread of Pine Wilt Disease

1The Academy of Forest, Beijing Forest University, Beijing 100083, China
2College of Mathematics and Information Science, Xinyang Normal University, Xinyang, Henan 64000, China
3School of Science, Beijing University of Civil Engineering and Architecture, Beijing 100044, China

Received 5 December 2012; Accepted 22 January 2013

Academic Editor: Francisco J. Marcellán

Copyright © 2013 Xiangyun Shi and Guohua Song. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper formulates and analyzes a pine wilt disease model. Mathematical analyses of the model with regard to invariance of nonnegativity, boundedness of the solutions, existence of nonnegative equilibria, permanence, and global stability are presented. It is proved that the global dynamics are determined by the basic reproduction number and the other value which is larger than . If and are both less than one, the disease-free equilibrium is asymptotically stable and the pine wilt disease always dies out. If one is between the two values, though the pine wilt disease could occur, the outbreak will stop. If the basic reproduction number is greater than one, a unique endemic equilibrium exists and is globally stable in the interior of the feasible region, and the disease persists at the endemic equilibrium state if it initially exists. Numerical simulations are carried out to illustrate the theoretical results, and some disease control measures are especially presented by these theoretical results.