IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v431y2022ics0096300322004039.html
   My bibliography  Save this article

A stochastic SIQR epidemic model with Lévy jumps and three-time delays

Author

Listed:
  • Zhang, Ge
  • Li, Zhiming
  • Din, Anwarud

Abstract

Isolation and vaccination are the two most effective measures in protecting the public from the spread of illness. The SIQR model with vaccination is widely used to investigate the dynamics of an infectious disease at population level having the compartments: susceptible, infectious, quarantined and recovered. The paper mainly aims to extend the deterministic model to a stochastic SQIR case with Lévy jumps and three-time delays, which is more suitable for modeling complex and instable environment. The existence and uniqueness of the global positive solution are obtained by using the Lyapunov method. The dynamic properties of stochastic solution are studied around the disease-free and endemic equilibria of the deterministic model. Our results reveal that stochastic perturbation affect the asymptotic properties of the model. Numerical simulation shows the effects of interested parameters of theoretical results, including quarantine, vaccination and jump parameters. Finally, we apply both the stochastic and deterministic models to analyze the outbreak of mutant COVID-19 epidemic in Gansu Province, China.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:431:y:2022:i:c:s0096300322004039
    DOI: 10.1016/j.amc.2022.127329
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300322004039
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2022.127329?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. Din, Anwarud & Li, Yongjin & Khan, Tahir & Zaman, Gul, 2020. "Mathematical analysis of spread and control of the novel corona virus (COVID-19) in China," Chaos, Solitons & Fractals, Elsevier, vol. 141(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. Wang, Tianlei & Hu, Zhixing & Liao, Fucheng & Ma, Wanbiao, 2013. "Global stability analysis for delayed virus infection model with general incidence rate and humoral immunity," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 89(C), pages 13-22.
    4. Yanli Ma & Jia-Bao Liu & Haixia Li, 2018. "Global Dynamics of an SIQR Model with Vaccination and Elimination Hybrid Strategies," Mathematics, MDPI, vol. 6(12), pages 1-12, December.
    5. Zhang, Xinhong & Jiang, Daqing & Hayat, Tasawar & Ahmad, Bashir, 2017. "Dynamics of a stochastic SIS model with double epidemic diseases driven by Lévy jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 767-777.
    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. Caraballo, Tomás & Settati, Adel & Fatini, Mohamed El & Lahrouz, Aadil & Imlahi, Abdelouahid, 2019. "Global stability and positive recurrence of a stochastic SIS model with Lévy noise perturbation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 677-690.
    8. Berrhazi, Badr-eddine & El Fatini, Mohamed & Laaribi, Aziz & Pettersson, Roger, 2018. "A stochastic viral infection model driven by Lévy noise," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 446-452.
    9. Bao, Kangbo & Zhang, Qimin & Rong, Libin & Li, Xining, 2019. "Dynamics of an imprecise SIRS model with Lévy jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 520(C), pages 489-506.
    10. 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).
    11. Fan, Kuangang & Zhang, Yan & Gao, Shujing & Chen, Shihua, 2020. "A delayed vaccinated epidemic model with nonlinear incidence rate and Lévy jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 544(C).
    12. Xu, Changyong & Li, Xiaoyue, 2018. "The threshold of a stochastic delayed SIRS epidemic model with temporary immunity and vaccination," Chaos, Solitons & Fractals, Elsevier, vol. 111(C), pages 227-234.
    13. 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.
    14. Din, Anwarud & Li, Yongjin & Yusuf, Abdullahi, 2021. "Delayed hepatitis B epidemic model with stochastic analysis," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    15. Tinggui Chen & Jiawen Shi & Jianjun Yang & Guodong Cong & Gongfa Li, 2020. "Modeling Public Opinion Polarization in Group Behavior by Integrating SIRS-Based Information Diffusion Process," Complexity, Hindawi, vol. 2020, pages 1-20, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Moualkia, Seyfeddine, 2023. "Mathematical analysis of new variant Omicron model driven by Lévy noise and with variable-order fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    2. Zhang, Ge & Li, Zhiming & Din, Anwarud & Chen, Tao, 2024. "Dynamic analysis and optimal control of a stochastic COVID-19 model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 215(C), pages 498-517.
    3. Song, Yi & Xu, Wei & Wei, Wei & Niu, Lizhi, 2023. "Dynamical transition of phenotypic states in breast cancer system with Lévy noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 627(C).
    4. Moualkia, Seyfeddine & Liu, Yang & Qiu, Jianlong & Lu, Jianquan, 2024. "An averaging result for fractional variable-order neutral differential equations with variable delays driven by Markovian switching and Lévy noise," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    5. RabieiMotlagh, Omid & Soleimani, Leila, 2023. "Effect of mutations on stochastic dynamics of infectious diseases, a probability approach," Applied Mathematics and Computation, Elsevier, vol. 451(C).

    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, 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).
    2. Liu, Chao & Tian, Yilin & Chen, Peng & Cheung, Lora, 2024. "Stochastic dynamic effects of media coverage and incubation on a distributed delayed epidemic system with Lévy jumps," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    3. 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).
    4. 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).
    5. Sayed Murad Ali Shah & Yufeng Nie & Anwarud Din & Abdulwasea Alkhazzan, 2024. "Dynamics of Hepatitis B Virus Transmission with a Lévy Process and Vaccination Effects," Mathematics, MDPI, vol. 12(11), pages 1-24, May.
    6. El Attouga, Sanae & Bouggar, Driss & El Fatini, Mohamed & Hilbert, Astrid & Pettersson, Roger, 2023. "Lévy noise with infinite activity and the impact on the dynamic of an SIRS epidemic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 618(C).
    7. Alkhazzan, Abdulwasea & Wang, Jungang & Nie, Yufeng & Khan, Hasib & Alzabut, Jehad, 2024. "A novel SIRS epidemic model for two diseases incorporating treatment functions, media coverage, and three types of noise," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    8. Din, Anwarud & Li, Yongjin & Yusuf, Abdullahi, 2021. "Delayed hepatitis B epidemic model with stochastic analysis," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    9. 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.
    10. 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).
    11. 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.
    12. Benazzouz, Meryem & Caraballo, Tomás & El Fatini, Mohamed & Laaribi, Aziz, 2024. "Discontinuous stochastic modeling and discrete numerical approximation for Tuberculosis model with relapse," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    13. Qi, Haokun & Zhang, Shengqiang & Meng, Xinzhu & Dong, Huanhe, 2018. "Periodic solution and ergodic stationary distribution of two stochastic SIQS epidemic systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 223-241.
    14. Selvan, T. Tamil & Kumar, M., 2023. "Dynamics of a deterministic and a stochastic epidemic model combined with two distinct transmission mechanisms and saturated incidence rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 619(C).
    15. Xu, Jiang & Chen, Tao & Wen, Xiangdan, 2021. "Analysis of a Bailey–Dietz model for vector-borne disease under regime switching," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 580(C).
    16. Wang, Jinliang & Guo, Min & Liu, Xianning & Zhao, Zhitao, 2016. "Threshold dynamics of HIV-1 virus model with cell-to-cell transmission, cell-mediated immune responses and distributed delay," Applied Mathematics and Computation, Elsevier, vol. 291(C), pages 149-161.
    17. Moualkia, Seyfeddine, 2023. "Mathematical analysis of new variant Omicron model driven by Lévy noise and with variable-order fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    18. 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).
    19. Din, Anwarud, 2024. "Bifurcation analysis of a delayed stochastic HBV epidemic model: Cell-to-cell transmission," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    20. Wang, Liang & Jiang, Daqing, 2017. "Periodic solution for the stochastic chemostat with general response function," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 378-385.

    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:apmaco:v:431:y:2022:i:c:s0096300322004039. 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.