Nonlinear Dynamics

, Volume 59, Issue 3, pp 503–513 | Cite as

Dynamics of a novel nonlinear SIR model with double epidemic hypothesis and impulsive effects

  • Xinzhu Meng
  • Zhenqing Li
  • Xiaoling Wang


In this paper, the propagation of a nonlinear delay SIR epidemic using the double epidemic hypothesis is modeled. In the model, a system of impulsive functional differential equations is studied and the sufficient conditions for the global attractivity of the semi-trivial periodic solution are drawn. By use of new computational techniques for impulsive differential equations with delay, we prove that the system is permanent under appropriate conditions. The results show that time delay, pulse vaccination, and nonlinear incidence have significant effects on the dynamics behaviors of the model. The conditions for the control of the infection caused by viruses A and B are given.


Double epidemic hypothesis Permanence Nonlinear incidence Time delay SIR epidemic model 


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© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.State Key Laboratory of Vegetation and Environmental ChangeInstitute of Botany, Chinese Academy of SciencesBeijingPeople’s Republic of China
  2. 2.College of Information Science and EngineeringShandong University of Science and TechnologyQingdaoPeople’s Republic of China
  3. 3.College of AgronomyHenan University of Science and TechnologyLuoyangPeople’s Republic of China

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