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Global stability of an SEI model for plant diseases

  • Yuming Chen EMAIL logo and Junyuan Yang
Published/Copyright: April 26, 2016
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 66 Issue 1

Abstract

We propose an SEI epidemic model for plant diseases, which incorporates disease latency, disease-caused removal, and constant recruitment in both susceptible and exposed classes. Because of the recruitment and disease-caused removal, the total population is varying. It is shown that the model only has an endemic equilibrium and the equilibrium is globally stable.

Keywords: plant disease; equilibrium; stability; permanence; Lyapunov function
MSC: Primary 34D23; 92D30

Research is supported partially by the Natural Science and Engineering Research Council of Canada (NSERC), the Early Researcher Award (ERA) Program of Ontario, the One Hundred Talents Project of Shanxi Province, the Program of Key Disciplines in Shanxi Province (20111028), the NSF of China (11071283,11371313,61573016,61203228), the Sciences Foundation of Shanxi (2009011005-3), the Young Sciences Foundation of Shanxi (2011021001-1), and the Foundation of University (YQ-2011045, JY-2011036).

  1. This paper has been communicated by Christian Pötzsche.

Acknowledgement

We would like to thank the anonymous reviewer for his helpful comments on improving the presentation of this paper. This work was done when Yang was a postdoctoral fellow at the Department of Mathematics, Wilfrid Laurier University. He would like to thank the Department for the hospitality.

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Received: 2012-9-28
Accepted: 2013-5-6
Published Online: 2016-4-26
Published in Print: 2016-2-1

© 2016 Mathematical Institute Slovak Academy of Sciences

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https://doi.org/10.1515/ms-2015-0137
Keywords for this article
plant disease; equilibrium; stability; permanence; Lyapunov function

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  5. Research Article
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