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Seasonality and mixed vaccination strategy in an epidemic model with vertical transmission

Author

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  • Gao, Shujing
  • Liu, Yujiang
  • Nieto, Juan J.
  • Andrade, Helena

Abstract

First vaccination (vaccinate at birth) and pulse vaccination are two methods used to control the spread of diseases as well as the elimination of them. Owing to the seasonal fluctuations in transmission of many diseases, we propose an impulsive SIRS epidemic model with periodic saturation incidence and vertical transmission. The effects of periodic varying contact rate and mixed vaccination strategy on eradication of infectious diseases are studied. A threshold for a disease to be extinct or endemic is established. Our results imply that the diseases will die out eventually if the basic reproduction number is less than unity, whereas the diseases will persist if the basic reproduction number is larger than unity. Finally, numerical simulations support our analytical conclusions.

Suggested Citation

  • Gao, Shujing & Liu, Yujiang & Nieto, Juan J. & Andrade, Helena, 2011. "Seasonality and mixed vaccination strategy in an epidemic model with vertical transmission," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(9), pages 1855-1868.
    • Handle: RePEc:eee:matcom:v:81:y:2011:i:9:p:1855-1868
    DOI: 10.1016/j.matcom.2010.10.032
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    Cited by:

    1. Liu, Lidan & Meng, Xinzhu & Zhang, Tonghua, 2017. "Optimal control strategy for an impulsive stochastic competition system with time delays and jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 477(C), pages 99-113.
    2. Gao, Shujing & Zhong, Deming & Zhang, Yan, 2018. "Analysis of novel stochastic switched SILI epidemic models with continuous and impulsive control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 495(C), pages 162-171.
    3. Guo, Zun-Guang & Sun, Gui-Quan & Wang, Zhen & Jin, Zhen & Li, Li & Li, Can, 2020. "Spatial dynamics of an epidemic model with nonlocal infection," Applied Mathematics and Computation, Elsevier, vol. 377(C).
    4. De la Sen, M. & Alonso-Quesada, S. & Ibeas, A. & Nistal, R., 2019. "On an SEIADR epidemic model with vaccination, treatment and dead-infectious corpses removal controls," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 163(C), pages 47-79.
    5. Liu, Qun & Jiang, Daqing, 2016. "The threshold of a stochastic delayed SIR epidemic model with vaccination," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 140-147.

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