## 摘要

In this paper, we study the dynamics of an SIR epidemic model with a logistic process and a distributed time delay. We first show that the attractivity of the disease-free equilibrium is completely determined by a threshold R _{0}. If R _{0}≤1, then the disease-free equilibrium is globally attractive and the disease always dies out. Otherwise, if R _{0}>1, then the disease-free equilibrium is unstable, and meanwhile there exists uniquely an endemic equilibrium. We then prove that for any time delay h>0, the delayed SIR epidemic model is permanent if and only if there exists an endemic equilibrium. In other words, R _{0}>1 is a necessary and sufficient condition for the permanence of the epidemic model. Numerical examples are given to illustrate the theoretical results. We also make a distinction between the dynamics of the distributed time delay system and the discrete time delay system.

原文 | ???core.languages.en_GB??? |
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頁（從 - 到） | 3696-3707 |

頁數 | 12 |

期刊 | Communications in Nonlinear Science and Numerical Simulation |

卷 | 17 |

發行號 | 9 |

DOIs | |

出版狀態 | 已出版 - 9月 2012 |