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Mathematical Biosciences and Engineering

2006, Volume 3, Issue 1: 101-109. doi: 10.3934/mbe.2006.3.101
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The stability of an SIR epidemic model with time delays

  • 1.
    Department of mathematics, North University of China, Taiyuan 030051, PR
  • 2.
    Department of Applied Mathematics, Xi'an Jiaotong University, Xi'an 710049, PR
  • Received: 01 December 2005 Accepted: 29 June 2018 Published: 01 November 2005

  • MSC : 92D30, 34K20, 34K25.

  • In this paper, an SIR epidemic model for the spread of an infectious disease transmitted by direct contact among humans and vectors (mosquitoes) which have an incubation time to become infectious is formulated. It is shown that a disease-free equilibrium point is globally stable if no endemic equilibrium point exists. Further, the endemic equilibrium point (if it exists) is globally stable with respect to a ''weak delay''. Some known results are generalized.

    Citation: Zhen Jin, Zhien Ma. The stability of an SIR epidemic model with time delays[J]. Mathematical Biosciences and Engineering, 2006, 3(1): 101-109. doi: 10.3934/mbe.2006.3.101

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  • In this paper, an SIR epidemic model for the spread of an infectious disease transmitted by direct contact among humans and vectors (mosquitoes) which have an incubation time to become infectious is formulated. It is shown that a disease-free equilibrium point is globally stable if no endemic equilibrium point exists. Further, the endemic equilibrium point (if it exists) is globally stable with respect to a ''weak delay''. Some known results are generalized.


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  • © 2006 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

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