The stability of an SIR epidemic model with time delays

Zhen Jin; Zhien Ma

doi:10.3934/mbe.2006.3.101

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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

Zhen Jin^1, and
Zhien Ma²

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: November 30, 2005

Revised: February 28, 2005

Published: October 2005

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Abstract

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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Mathematics Subject Classification: 92D30, 34K20, 34K25.

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