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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

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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Keywords 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. Mathematical Biosciences and Engineering, 2006, 3(1): 101-109. doi: 10.3934/mbe.2006.3.101


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Copyright Info: 2006, Zhen Jin, et al., licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

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