Journal of Guangxi Normal University(Natural Science Edition) ›› 2017, Vol. 35 ›› Issue (2): 58-65.doi: 10.16088/j.issn.1001-6600.2017.02.009

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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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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

CLC Number: 

  • O175.14
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