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

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  • Tongqian Zhang
  • Xinzhu Meng
  • Tonghua Zhang

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.

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  • Tongqian Zhang & Xinzhu Meng & Tonghua Zhang, 2014. "SVEIRS: A New Epidemic Disease Model with Time Delays and Impulsive Effects," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-15, May.
    • Handle: RePEc:hin:jnlaaa:542154
    DOI: 10.1155/2014/542154
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    Cited by:

    1. Liu, Qun & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed, 2018. "Stationary distribution of a stochastic delayed SVEIR epidemic model with vaccination and saturation incidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 849-863.

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