IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v143y2021ics0960077920309310.html
   My bibliography  Save this article

Stochastic dynamical probes in a triple delayed SICR model with general incidence rate and immunization strategies

Author

Listed:
  • M, Pitchaimani
  • M, Brasanna Devi

Abstract

Disease transmission play prominent role in the course of infection dynamics in any epidemic outbreak. A mathematical probe on the stochastic dynamics of SICR model structure with generalized incidence rate and three time delays forms the crux of this article. With Lyapunov theory, the existence of unique positive global solution, and the predictable lanes for both the extinction and persistence of disease in the community have been explored. Also, we exemplify the existence of unique ergodic stationary distribution in the system. Theoretical establishments are supplemented with numerical substantiations to depict real dynamics.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:143:y:2021:i:c:s0960077920309310
    DOI: 10.1016/j.chaos.2020.110540
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077920309310
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2020.110540?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Liu, Qun & Jiang, Daqing, 2019. "Dynamical behavior of a stochastic multigroup SIR epidemic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 526(C).
    2. Qiuhua Zhang & Kai Zhou, 2019. "Stationary Distribution and Extinction of a Stochastic SIQR Model with Saturated Incidence Rate," Mathematical Problems in Engineering, Hindawi, vol. 2019, pages 1-12, June.
    3. 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.
    4. M., Pitchaimani & M., Brasanna Devi, 2020. "Random effects in HIV infection model at Eclipse stage," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 554(C).
    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.
    6. Liu, Qun & Jiang, Daqing & Shi, Ningzhong & Hayat, Tasawar, 2018. "Dynamics of a stochastic delayed SIR epidemic model with vaccination and double diseases driven by Lévy jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 492(C), pages 2010-2018.
    7. Cao, Zhongwei & Feng, Wei & Wen, Xiangdan & Zu, Li & Cheng, Ming, 2019. "Dynamics of a stochastic SIQR epidemic model with standard incidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 527(C).
    8. 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.
    9. 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.
    10. Fan, Kuangang & Zhang, Yan & Gao, Shujing & Wei, Xiang, 2017. "A class of stochastic delayed SIR epidemic models with generalized nonlinear incidence rate and temporary immunity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 481(C), pages 198-208.
    11. Berrhazi, Badr-eddine & El Fatini, Mohamed & Laaribi, Aziz & Pettersson, Roger & Taki, Regragui, 2017. "A stochastic SIRS epidemic model incorporating media coverage and driven by Lévy noise," Chaos, Solitons & Fractals, Elsevier, vol. 105(C), pages 60-68.
    12. Liu, Qun & Chen, Qingmei & Jiang, Daqing, 2016. "The threshold of a stochastic delayed SIR epidemic model with temporary immunity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 450(C), pages 115-125.
    13. Hattaf, Khalid & Mahrouf, Marouane & Adnani, Jihad & Yousfi, Noura, 2018. "Qualitative analysis of a stochastic epidemic model with specific functional response and temporary immunity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 591-600.
    14. Zhongwei Cao & Shengjuan Zhou, 2018. "Dynamical Behaviors of a Stochastic SIQR Epidemic Model with Quarantine-Adjusted Incidence," Discrete Dynamics in Nature and Society, Hindawi, vol. 2018, pages 1-13, March.
    15. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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).
    3. Berrhazi, Badr-eddine & El Fatini, Mohamed & Laaribi, Aziz, 2018. "A stochastic threshold for an epidemic model with Beddington–DeAngelis incidence, delayed loss of immunity and Lévy noise perturbation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 507(C), pages 312-320.
    4. Zhang, Ge & Li, Zhiming & Din, Anwarud, 2022. "A stochastic SIQR epidemic model with Lévy jumps and three-time delays," Applied Mathematics and Computation, Elsevier, vol. 431(C).
    5. Zhang, Zizhen & Kundu, Soumen & Tripathi, Jai Prakash & Bugalia, Sarita, 2020. "Stability and Hopf bifurcation analysis of an SVEIR epidemic model with vaccination and multiple time delays," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    6. Jia, Pingqi & Wang, Chao & Zhang, Gaoyu & Ma, Jianfeng, 2019. "A rumor spreading model based on two propagation channels in social networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 524(C), pages 342-353.
    7. Wanduku, Divine, 2017. "Complete global analysis of a two-scale network SIRS epidemic dynamic model with distributed delay and random perturbations," Applied Mathematics and Computation, Elsevier, vol. 294(C), pages 49-76.
    8. 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).
    9. Liu, Yue, 2022. "Extinction, persistence and density function analysis of a stochastic two-strain disease model with drug resistance mutation," Applied Mathematics and Computation, Elsevier, vol. 433(C).
    10. Fan, Kuangang & Zhang, Yan & Gao, Shujing & Wei, Xiang, 2017. "A class of stochastic delayed SIR epidemic models with generalized nonlinear incidence rate and temporary immunity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 481(C), pages 198-208.
    11. Hattaf, Khalid & Mahrouf, Marouane & Adnani, Jihad & Yousfi, Noura, 2018. "Qualitative analysis of a stochastic epidemic model with specific functional response and temporary immunity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 591-600.
    12. Cao, Zhongwei & Shi, Yuee & Wen, Xiangdan & Liu, Liya & Hu, Jingwei, 2020. "Analysis of a hybrid switching SVIR epidemic model with vaccination and Lévy noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).
    13. Zhang, Xiao-Bing & Huo, Hai-Feng & Xiang, Hong & Shi, Qihong & Li, Dungang, 2017. "The threshold of a stochastic SIQS epidemic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 482(C), pages 362-374.
    14. 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.
    15. 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.
    16. 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).
    17. 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.
    18. Utsumi, Shinobu & Arefin, Md. Rajib & Tatsukawa, Yuichi & Tanimoto, Jun, 2022. "How and to what extent does the anti-social behavior of violating self-quarantine measures increase the spread of disease?," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    19. Sun, Shulin & Zhang, Xiaofeng, 2018. "Asymptotic behavior of a stochastic delayed chemostat model with nonmonotone uptake function," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 38-56.
    20. Chen, Xingzhi & Xu, Xin & Tian, Baodan & Li, Dong & Yang, Dan, 2022. "Dynamics of a stochastic delayed chemostat model with nutrient storage and Lévy jumps," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:143:y:2021:i:c:s0960077920309310. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.