广西师范大学学报（自然科学版） ›› 2017, Vol. 35 ›› Issue (2): 58-65.doi: 10.16088/j.issn.1001-6600.2017.02.009

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具有非线性传染率及脉冲免疫接种的SIQR传染病模型

邢伟1, 高晋芳2, 颜七笙1*, 周其华1   

  1. 1.东华理工大学理学院,江西南昌330013;
    2.华东交通大学理工学院,江西南昌330013
  • 出版日期:2017-07-25 发布日期:2018-07-25
  • 通讯作者: 颜七笙(1975—),男,江西临川人,东华理工大学教授,博士。E-mail:qshyan@ecit.cn
  • 基金资助:
    国家自然科学基金(11661005);江西省高等学校教学改革研究项目(JXJG-15-6-22);江西省教育厅科学技术研究项目(GJJ14469)

An SIQR Epidemic Model with Nonlinear Incidence Rateand Impulsive Vaccination

XING Wei1,GAO Jinfang2,YAN Qisheng1*,ZHOU Qihua1   

  1. 1.School of Science,East China University of Technology,Nanchang Jiangxi 330013,China;
    2.Institute of Technology,East China Jiaotong University,Nanchang Jiangxi 330013,China
  • Online:2017-07-25 Published:2018-07-25

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摘要： 本文研究了具有非线性传染率及脉冲免疫接种的SIQR模型,采用非线性传染率βI(t)(1+vI(t))S(t)得到了疾病流行与否的阈值,并且利用Floquet定理及比较定理证明了无病周期解的存在性与全局渐近稳定性,最后讨论了系统疾病一致持续的充分条件。研究结果表明:当参数满足一些条件时,疾病永久存在不会消亡,丰富了传染病动力学的理论知识。

关键词: 非线性传染率, SIQR模型, 全局渐近稳定性, 一致持续

Abstract: An SIQR epidemic model with vertical transmission and impulsive vaccination is investigated in this paper. Nonlinear infection rate of βI(t)(1+vI(t))S(t) is used and the threshold of disease popularity is obtained. The Floquet theorem and the comparison theorem are used to prove the existence and globally asymptotical stability of the disease-free periodic solution. Sufficient conditions for the uniform persistence of the system are obtained in the end.The results show that when the parameters satisfy some conditions, the disease does not perish.At the same time, the knowledge of dynamics of infectious diseases is enriched.

Key words: nonlinear incidence rate, SIQR model, globally asymptotical stability, uniform persistence

中图分类号: 

  • O175.14
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