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Dynamical behavior of a stochastic SVIR epidemic model with vaccination

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  • Zhang, Xinhong
  • Jiang, Daqing
  • Hayat, Tasawar
  • Ahmad, Bashir

Abstract

In this paper, we investigate the dynamical behavior of SVIR models in random environments. Firstly, we show that if R0s<1, the disease of stochastic autonomous SVIR model will die out exponentially; if R̃0s>1, the disease will be prevail. Moreover, this system admits a unique stationary distribution and it is ergodic when R̃0s>1. Results show that environmental white noise is helpful for disease control. Secondly, we give sufficient conditions for the existence of nontrivial periodic solutions to stochastic SVIR model with periodic parameters. Finally, numerical simulations validate the analytical results.

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  • Zhang, Xinhong & Jiang, Daqing & Hayat, Tasawar & Ahmad, Bashir, 2017. "Dynamical behavior of a stochastic SVIR epidemic model with vaccination," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 483(C), pages 94-108.
    • Handle: RePEc:eee:phsmap:v:483:y:2017:i:c:p:94-108
    DOI: 10.1016/j.physa.2017.04.173
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    References listed on IDEAS

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    Cited by:

    1. Lu, Ruoxin & Wei, Fengying, 2019. "Persistence and extinction for an age-structured stochastic SVIR epidemic model with generalized nonlinear incidence rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 513(C), pages 572-587.
    2. Zhang, Xinhong & Shi, Zhenfeng & Wang, Yuanyuan, 2019. "Dynamics of a stochastic avian–human influenza epidemic model with mutation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(C).
    3. Zhou, Baoquan & Zhang, Xinhong & Jiang, Daqing, 2020. "Dynamics and density function analysis of a stochastic SVI epidemic model with half saturated incidence rate," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    4. Han, Bingtao & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed & Ahmad, Bashir, 2020. "Stationary distribution and extinction of a stochastic staged progression AIDS model with staged treatment and second-order perturbation," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    5. Zhang, Xiao-Bing & Chang, Suqin & Shi, Qihong & Huo, Hai-Feng, 2018. "Qualitative study of a stochastic SIS epidemic model with vertical transmission," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 805-817.
    6. M, Pitchaimani & M, Brasanna Devi, 2021. "Stochastic dynamical probes in a triple delayed SICR model with general incidence rate and immunization strategies," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    7. Li, Xiao-Ping & Din, Anwarud & Zeb, Anwar & Kumar, Sunil & Saeed, Tareq, 2022. "The impact of Lévy noise on a stochastic and fractal-fractional Atangana–Baleanu order hepatitis B model under real statistical data," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    8. Zhou, Baoquan & Jiang, Daqing & Dai, Yucong & Hayat, Tasawar & Alsaedi, Ahmed, 2021. "Stationary distribution and probability density function of a stochastic SVIS epidemic model with standard incidence and vaccination strategies," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    9. Alkhazzan, Abdulwasea & Wang, Jungang & Nie, Yufeng & Khan, Hasib & Alzabut, Jehad, 2023. "An effective transport-related SVIR stochastic epidemic model with media coverage and Lévy noise," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    10. Zhou, Baoquan & Jiang, Daqing & Han, Bingtao & Hayat, Tasawar, 2022. "Threshold dynamics and density function of a stochastic epidemic model with media coverage and mean-reverting Ornstein–Uhlenbeck process," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 196(C), pages 15-44.
    11. Han, Bingtao & Zhou, Baoquan & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed, 2021. "Stationary solution, extinction and density function for a high-dimensional stochastic SEI epidemic model with general distributed delay," Applied Mathematics and Computation, Elsevier, vol. 405(C).
    12. Lin Hu & Lin-Fei Nie, 2022. "Dynamics of a Stochastic HIV Infection Model with Logistic Growth and CTLs Immune Response under Regime Switching," Mathematics, MDPI, vol. 10(19), pages 1-20, September.
    13. Rajasekar, S.P. & Pitchaimani, M., 2019. "Qualitative analysis of stochastically perturbed SIRS epidemic model with two viruses," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 207-221.
    14. El Fatini, Mohamed & Sekkak, Idriss & Laaribi, Aziz, 2019. "A threshold of a delayed stochastic epidemic model with Crowly–Martin functional response and vaccination," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 520(C), pages 151-160.
    15. Lan, Guijie & Chen, Zhewen & Wei, Chunjin & Zhang, Shuwen, 2018. "Stationary distribution of a stochastic SIQR epidemic model with saturated incidence and degenerate diffusion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 511(C), pages 61-77.

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