Abstract and Applied Analysis

SVEIRS: A New Epidemic Disease Model with Time Delays and Impulsive Effects

Tongqian Zhang, Xinzhu Meng, and Tonghua Zhang

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Abstract

We first propose a new epidemic disease model governed by system of impulsive delay differential equations. Then, based on theories for impulsive delay differential equations, we skillfully solve the difficulty in analyzing the global dynamical behavior of the model with pulse vaccination and impulsive population input effects at two different periodic moments. We prove the existence and global attractivity of the “infection-free” periodic solution and also the permanence of the model. We then carry out numerical simulations to illustrate our theoretical results, showing us that time delay, pulse vaccination, and pulse population input can exert a significant influence on the dynamics of the system which confirms the availability of pulse vaccination strategy for the practical epidemic prevention. Moreover, it is worth pointing out that we obtained an epidemic control strategy for controlling the number of population input.

Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 542154, 15 pages.

Dates
First available in Project Euclid: 3 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412360635

Digital Object Identifier
doi:10.1155/2014/542154

Mathematical Reviews number (MathSciNet)
MR3216058

Zentralblatt MATH identifier
07022589

Citation

Zhang, Tongqian; Meng, Xinzhu; Zhang, Tonghua. SVEIRS: A New Epidemic Disease Model with Time Delays and Impulsive Effects. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 542154, 15 pages. doi:10.1155/2014/542154. https://projecteuclid.org/euclid.aaa/1412360635


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