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Stationary distribution of a stochastic delayed SVEIR epidemic model with vaccination and saturation incidence

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  • Liu, Qun
  • Jiang, Daqing
  • Hayat, Tasawar
  • Alsaedi, Ahmed

Abstract

In this paper, we develop and analyze a stochastic delayed SVEIR epidemic model with vaccination and saturation incidence. By constructing a suitable stochastic Lyapunov function, we establish sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the positive solutions to the model. The existence of a stationary distribution implies stochastic weak stability. Numerical simulations are introduced to illustrate the analytical result.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:512:y:2018:i:c:p:849-863
    DOI: 10.1016/j.physa.2018.08.054
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    References listed on IDEAS

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    1. Chang, Zhengbo & Meng, Xinzhu & Lu, Xiao, 2017. "Analysis of a novel stochastic SIRS epidemic model with two different saturated incidence rates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 472(C), pages 103-116.
    2. 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.
    3. Liu, Qun & Jiang, Daqing & Shi, Ningzhong & Hayat, Tasawar & Ahmad, Bashir, 2017. "Stationary distribution and extinction of a stochastic SEIR epidemic model with standard incidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 476(C), pages 58-69.
    4. Yu, Jingyi & Liu, Meng, 2017. "Stationary distribution and ergodicity of a stochastic food-chain model with Lévy jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 482(C), pages 14-28.
    5. Cai, Yongli & Kang, Yun & Wang, Weiming, 2017. "A stochastic SIRS epidemic model with nonlinear incidence rate," Applied Mathematics and Computation, Elsevier, vol. 305(C), pages 221-240.
    6. Wang, Lianwen & Liu, Zhijun & Zhang, Xingan, 2016. "Global dynamics of an SVEIR epidemic model with distributed delay and nonlinear incidence," Applied Mathematics and Computation, Elsevier, vol. 284(C), pages 47-65.
    7. Yan Wang & Daqing Jiang, 2017. "Stationary Distribution and Extinction of a Stochastic Viral Infection Model," Discrete Dynamics in Nature and Society, Hindawi, vol. 2017, pages 1-13, October.
    8. Liu, Qun & Jiang, Daqing & Shi, Ningzhong & Hayat, Tasawar & Alsaedi, Ahmed, 2017. "Stationary distribution and extinction of a stochastic SIRS epidemic model with standard incidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 469(C), pages 510-517.
    9. Liu, Qun & Chen, Qingmei, 2015. "Analysis of the deterministic and stochastic SIRS epidemic models with nonlinear incidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 428(C), pages 140-153.
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    Cited by:

    1. Xu, Dongsheng & Liu, Ming & Xu, Xiaofeng, 2020. "Analysis of a stochastic predator–prey system with modified Leslie–Gower and Holling-type IV schemes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).
    2. Wang, Lei & Teng, Zhidong & Ji, Chunyan & Feng, Xiaomei & Wang, Kai, 2019. "Dynamical behaviors of a stochastic malaria model: A case study for Yunnan, China," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 435-454.
    3. Settati, A. & Lahrouz, A. & Assadouq, A. & El Fatini, M. & El Jarroudi, M. & Wang, K., 2020. "The impact of nonlinear relapse and reinfection to derive a stochastic threshold for SIRI epidemic model," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).

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