Global Dynamics Behaviors for a New Delay SEIR Epidemic Disease Model With Vertical Transmission and Pulse Vaccination

MENG Xin-zhu; CHEN Lan-sun; SONG Zhi-tao

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Article Navigation > Applied Mathematics and Mechanics > 2007 > 28(9): 1123-1134

MENG Xin-zhu, CHEN Lan-sun, SONG Zhi-tao. Global Dynamics Behaviors for a New Delay SEIR Epidemic Disease Model With Vertical Transmission and Pulse Vaccination[J]. Applied Mathematics and Mechanics, 2007, 28(9): 1123-1134.

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Global Dynamics Behaviors for a New Delay SEIR Epidemic Disease Model With Vertical Transmission and Pulse Vaccination

1.
College of Science, Shandong University of Science and Technology, Qingdao 266510, P. R. China;

Received Date: 2007-01-23
Rev Recd Date: 2007-04-16
Publish Date: 2007-09-15

Abstract

Abstract

A robust SEIR epidemic disease model with a profitless delay and vertical transmission was formulated, and the dynamics behaviors of the model under pulse vaccination were analyzed. By use of the discrete dynamical system determined by the stroboscopic map, an infection-free. periodic solution was 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, sufficient condition with time delay for the permanence of the system was obtained. And it was 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".
- permanence,
- pulse vaccination,
- horizontal and vertical transmission,
- delay,
- global attractivity

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References(28)

References

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