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Behavior of a stochastic SIR epidemic model with saturated incidence and vaccination rules

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  • Zhang, Yue
  • Li, Yang
  • Zhang, Qingling
  • Li, Aihua

Abstract

In this paper, the threshold behavior of a susceptible–infected–recovered (SIR) epidemic model with stochastic perturbation is investigated. Firstly, it is obtained that the system has a unique global positive solution with any positive initial value. Random effect may lead to disease extinction under a simple condition. Subsequently, sufficient condition for persistence has been established in the mean of the disease. Finally, some numerical simulations are carried out to confirm the analytical results.

Suggested Citation

  • Zhang, Yue & Li, Yang & Zhang, Qingling & Li, Aihua, 2018. "Behavior of a stochastic SIR epidemic model with saturated incidence and vaccination rules," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 501(C), pages 178-187.
    • Handle: RePEc:eee:phsmap:v:501:y:2018:i:c:p:178-187
    DOI: 10.1016/j.physa.2018.02.191
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    References listed on IDEAS

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    Cited by:

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    2. Turkyilmazoglu, Mustafa, 2022. "An extended epidemic model with vaccination: Weak-immune SIRVI," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 598(C).
    3. Bobryk, R.V., 2021. "Stability analysis of a SIR epidemic model with random parametric perturbations," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    4. 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.
    5. El Fatini, Mohamed & Sekkak, Idriss, 2020. "Lévy noise impact on a stochastic delayed epidemic model with Crowly–Martin incidence and crowding effect," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 541(C).
    6. 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.
    7. Okita, Kouki & Tatsukawa, Yuichi & Utsumi, Shinobu & Arefin, Md. Rajib & Hossain, Md. Anowar & Tanimoto, Jun, 2023. "Stochastic resonance effect observed in a vaccination game with effectiveness framework obeying the SIR process on a scale-free network," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    8. Jin, Xihua & Jia, Jianwen, 2020. "Qualitative study of a stochastic SIRS epidemic model with information intervention," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 547(C).
    9. Qi, Haokun & Meng, Xinzhu, 2021. "Mathematical modeling, analysis and numerical simulation of HIV: The influence of stochastic environmental fluctuations on dynamics," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 187(C), pages 700-719.

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