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Journal of Applied Mathematics
Volume 2014, Article ID 204241, 9 pages
http://dx.doi.org/10.1155/2014/204241
Research Article

Analysis of Pine Wilt Disease Model with Nonlinear Incidence and Horizontal Transmission

School of Natural Sciences, National University of Sciences and Technology, H-12, Islamabad, Pakistan

Received 25 January 2014; Accepted 30 April 2014; Published 9 June 2014

Academic Editor: Xinyu Song

Copyright © 2014 Muhammad Ozair. 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.

Abstract

The deterministic pine wilt model with vital dynamics to determine the equilibria and their stability by considering nonlinear incidence rates with horizontal transmission is analyzed. The complete global analysis for the equilibria of the model is discussed. The explicit formula for the reproductive number is obtained and it is shown that the “disease-free” equilibrium always exists and is globally asymptotically stable whenever . Furthermore, the disease persists at an “endemic” level when the reproductive number exceeds unity.