Analysis of the permanence of an SIR epidemic model with logistic process and distributed time delay

Chun Hsien Li, Chiung Chiou Tsai, Suh Yuh Yang

研究成果: 雜誌貢獻期刊論文同行評審

19 引文 斯高帕斯(Scopus)

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???
頁(從 - 到)3696-3707
頁數12
期刊Communications in Nonlinear Science and Numerical Simulation
17
發行號9
DOIs
出版狀態已出版 - 9月 2012

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