The stability of an SIR epidemic model with time delays

2006, Volume 3, Issue 1: 101-109. doi: 10.3934/mbe.2006.3.101

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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.
- global asymptotic stability,
- time delay,
- Lyapunov functional.,
- SIR epidemic model
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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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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