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Periodic solution and stationary distribution of stochastic SIR epidemic models with higher order perturbation

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  • Liu, Qun
  • Jiang, Daqing
  • Hayat, Tasawar
  • Ahmad, Bashir

Abstract

In this paper, we investigate two stochastic SIR epidemic models with higher order perturbation. For the nonautonomous periodic case of the model, by using Has’minskii’s theory of periodic solution, we show that the system has at least one nontrivial positive T-periodic solution. For the system disturbed by both the white noise and telephone noise, we establish sufficient conditions for positive recurrence and the existence of ergodic stationary distribution of the positive solution.

Suggested Citation

  • Liu, Qun & Jiang, Daqing & Hayat, Tasawar & Ahmad, Bashir, 2017. "Periodic solution and stationary distribution of stochastic SIR epidemic models with higher order perturbation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 482(C), pages 209-217.
    • Handle: RePEc:eee:phsmap:v:482:y:2017:i:c:p:209-217
    DOI: 10.1016/j.physa.2017.04.056
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    References listed on IDEAS

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    1. Wang, Fengyan & Wang, Xiaoyi & Zhang, Shuwen & Ding, Changming, 2014. "On pulse vaccine strategy in a periodic stochastic SIR epidemic model," Chaos, Solitons & Fractals, Elsevier, vol. 66(C), pages 127-135.
    2. Liu, Qun & Jiang, Daqing & Shi, Ningzhong & Hayat, Tasawar & Alsaedi, Ahmed, 2016. "Nontrivial periodic solution of a stochastic non-autonomous SISV epidemic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 837-845.
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    Citations

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    Cited by:

    1. Zhou, Baoquan & Han, Bingtao & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed, 2021. "Ergodic stationary distribution and extinction of a hybrid stochastic SEQIHR epidemic model with media coverage, quarantine strategies and pre-existing immunity under discrete Markov switching," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    2. Sabbar, Yassine & Din, Anwarud & Kiouach, Driss, 2023. "Influence of fractal–fractional differentiation and independent quadratic Lévy jumps on the dynamics of a general epidemic model with vaccination strategy," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    3. Tingting Ma & Xinzhu Meng & Zhengbo Chang, 2019. "Dynamics and Optimal Harvesting Control for a Stochastic One-Predator-Two-Prey Time Delay System with Jumps," Complexity, Hindawi, vol. 2019, pages 1-19, March.
    4. Sabbar, Yassine & Kiouach, Driss & Rajasekar, S.P. & El-idrissi, Salim El Azami, 2022. "The influence of quadratic Lévy noise on the dynamic of an SIC contagious illness model: New framework, critical comparison and an application to COVID-19 (SARS-CoV-2) case," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    5. Zu, Li & Jiang, Daqing & O’Regan, Donal & Hayat, Tasawar & Ahmad, Bashir, 2018. "Ergodic property of a Lotka–Volterra predator–prey model with white noise higher order perturbation under regime switching," Applied Mathematics and Computation, Elsevier, vol. 330(C), pages 93-102.
    6. 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.
    7. Yassine Sabbar & Mehmet Yavuz & Fatma Özköse, 2022. "Infection Eradication Criterion in a General Epidemic Model with Logistic Growth, Quarantine Strategy, Media Intrusion, and Quadratic Perturbation," Mathematics, MDPI, vol. 10(22), pages 1-16, November.
    8. Liu, Qun & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed, 2019. "Stationary distribution of a regime-switching predator–prey model with anti-predator behaviour and higher-order perturbations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 199-210.
    9. Liu, Qun & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed, 2018. "Long-time behavior of a stochastic logistic equation with distributed delay and nonlinear perturbation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 289-304.
    10. Li, Sen & Su, Huan & Ding, Xiaohua, 2020. "The existence of inner synchronized stationary distribution for stochastic coupled systems on networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 538(C).
    11. Wen, Buyu & Teng, Zhidong & Li, Zhiming, 2018. "The threshold of a periodic stochastic SIVS epidemic model with nonlinear incidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 532-549.
    12. Liu, Qun & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed & Ahmad, Bashir, 2020. "Dynamical behavior of a higher order stochastically perturbed SIRI epidemic model with relapse and media coverage," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).

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