Applied Mathematics and Mechanics

, Volume 28, Issue 9, pp 1259–1271 | Cite as

Global dynamics behaviors for new delay SEIR epidemic disease model with vertical transmission and pulse vaccination

  • Meng Xin-zhu  (孟新柱)Email author
  • Chen Lan-sun  (陈兰荪)
  • Song Zhi-tao  (宋治涛)


A robust SEIR epidemic disease model with a profitless delay and vertical transmission is formulated, and the dynamics behaviors of the model under pulse vaccination are analyzed. By use of the discrete dynamical system determined by the stroboscopic map, an ‘infection-free’ periodic solution is obtained, further, it is shown that the ‘infection-free’ periodic solution is globally attractive when some parameters of the model are under appropriate conditions. Using the theory on delay functional and impulsive differential equation, the sufficient condition with time delay for the permanence of the system is obtained, and it is proved that time delays, pulse vaccination and vertical transmission can bring obvious effects on the dynamics behaviors of the model. The results indicate that the delay is ‘profitless’.

Key words

permanence pulse vaccination horizontal and vertical transmission delays global attractivity 

Chinese Library Classification


2000 Mathematics Subject Classification

92D30 34K20 34K25 


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Copyright information

© Editorial Committee of Appl. Math. Mech. 2007

Authors and Affiliations

  • Meng Xin-zhu  (孟新柱)
    • 1
    • 2
    Email author
  • Chen Lan-sun  (陈兰荪)
    • 2
  • Song Zhi-tao  (宋治涛)
    • 1
  1. 1.College of ScienceShandong University of Science and TechnologyQingdaoP. R. China
  2. 2.Department of Applied MathematicsDalian University of TechnologyDalianP. R. China

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