一类带有时滞和脉冲接种具有不同传染性SIR传染病模型动力学性质的研究

数学季刊 ›› 2010, Vol. 25 ›› Issue (2): 228-235.

一类带有时滞和脉冲接种具有不同传染性SIR传染病模型动力学性质的研究

Department of Mathematics, Huanghuai University

收稿日期:2009-07-19 出版日期:2010-06-30 发布日期:2023-06-05
作者简介: ZHANG Xiu-quan(1974-), male, native of Zhumadian, Henan, a lecturer of Huanghuai University, M.S.D., engages in biomathematics; ZHAO Zhong(1974-), male, native of Zhumadian, Henan, a lecturer of Huanghuai niversity, Ph.D., engages in biomathematics.
基金资助:
Supported by the National Natural Science Foundation of China(10971001)； Supported by Henan Science and Technology Department(082102140025,092300410228)；

Differential Susceptibility SIR Epidemic Model with Time Delay and Pulse Vaccination

Department of Mathematics, Huanghuai University

Received:2009-07-19 Online:2010-06-30 Published:2023-06-05
About author: ZHANG Xiu-quan(1974-), male, native of Zhumadian, Henan, a lecturer of Huanghuai University, M.S.D., engages in biomathematics; ZHAO Zhong(1974-), male, native of Zhumadian, Henan, a lecturer of Huanghuai niversity, Ph.D., engages in biomathematics.
Supported by:
Supported by the National Natural Science Foundation of China(10971001)； Supported by Henan Science and Technology Department(082102140025,092300410228)；

摘要/Abstract

摘要： Differential susceptibility SIR epidemic models with time delay and pulse vaccination is studied in this paper. We show that there exists an infection-free periodic solution by using the comparison method, which is globally attractive provided that R₁<1, and that R₂>1 implies the disease is permanent, which means that after some period of time the disease will become endemic.

关键词: impulsive vaccination, periodic solution, global attractivity, permanence

Abstract: Differential susceptibility SIR epidemic models with time delay and pulse vaccination is studied in this paper. We show that there exists an infection-free periodic solution by using the comparison method, which is globally attractive provided that R₁<1, and that R₂>1 implies the disease is permanent, which means that after some period of time the disease will become endemic.

Key words: impulsive vaccination, periodic solution, global attractivity, permanence

中图分类号:

O175.1

张秀全, 赵中. 一类带有时滞和脉冲接种具有不同传染性SIR传染病模型动力学性质的研究[J]. 数学季刊, 2010, 25(2): 228-235.

ZHANG Xiu-quan, ZHAO Zhong. Differential Susceptibility SIR Epidemic Model with Time Delay and Pulse Vaccination [J]. Chinese Quarterly Journal of Mathematics, 2010, 25(2): 228-235.

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