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Computational and Applied Mathematics

, Volume 35, Issue 2, pp 519–531 | Cite as

Control measures of pine wilt disease

  • Muhammad OzairEmail author
  • Xiangyun Shi
  • Takasar Hussain
Article

Abstract

In this paper, we study a vector–host model of pine wilt disease with vital dynamics to determine the equilibria and their stability by considering standard incidence rates and horizontal transmission. The complete global analysis for the equilibria of the model is analyzed. 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 \(R_{0}\le 1\). Furthermore, the disease persists at an “ endemic” level when the reproductive number exceeds unity. It will be very helpful in providing a theoretical basis for the prevention and control of the disease.

Keywords

Epidemic model Stability Sensitivity analysis 

Mathematics Subject Classification

34D23 

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Copyright information

© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2014

Authors and Affiliations

  1. 1.School of Natural SciencesNational University of Sciences and TechnologyIslamabadPakistan
  2. 2.Department of MathematicsXinyang Normal UniversityXinyangPeople’s Republic of China

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