IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i7p1712-d1114863.html
   My bibliography  Save this article

Stochastic Dynamics of a Virus Variant Epidemic Model with Double Inoculations

Author

Listed:
  • Hui Chen

    (Department of Mathematics, Yunnan Minzu University, 2929, Yuehua Street, Chenggong District, Kunming 650500, China
    These authors contributed equally to this work.)

  • Xuewen Tan

    (Department of Mathematics, Yunnan Minzu University, 2929, Yuehua Street, Chenggong District, Kunming 650500, China
    These authors contributed equally to this work.)

  • Jun Wang

    (Department of Mathematics, Yunnan Minzu University, 2929, Yuehua Street, Chenggong District, Kunming 650500, China)

  • Wenjie Qin

    (Department of Mathematics, Yunnan Minzu University, 2929, Yuehua Street, Chenggong District, Kunming 650500, China)

  • Wenhui Luo

    (Department of Mathematics, Yunnan Minzu University, 2929, Yuehua Street, Chenggong District, Kunming 650500, China)

Abstract

In this paper, we establish a random epidemic model with double vaccination and spontaneous variation of the virus. Firstly, we prove the global existence and uniqueness of positive solutions for a stochastic epidemic model. Secondly, we prove the threshold R 0 * can be used to control the stochastic dynamics of the model. If R 0 * < 0 , the disease will be extinct with probability 1; whereas if R 0 * > 0 , the disease can almost certainly continue to exist, and there is a unique stable distribution. Finally, we give some numerical examples to verify our theoretical results. Most of the existing studies prove the stochastic dynamics of the model by constructing Lyapunov functions. However, the construction of a Lyapunov function of higher-order models is extremely complex, so this method is not applicable to all models. In this paper, we use the definition method suitable for more models to prove the stationary distribution. Most of the stochastic infectious disease models studied now are second-order or third-order, and cannot accurately describe infectious diseases. In order to solve this kind of problem, this paper adopts a higher price five-order model.

Suggested Citation

  • Hui Chen & Xuewen Tan & Jun Wang & Wenjie Qin & Wenhui Luo, 2023. "Stochastic Dynamics of a Virus Variant Epidemic Model with Double Inoculations," Mathematics, MDPI, vol. 11(7), pages 1-29, April.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:7:p:1712-:d:1114863
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/7/1712/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/7/1712/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Bilgen Kaymakamzade & Evren Hincal, 2018. "Two-strain epidemic model with two vaccinations and two time delayed," Quality & Quantity: International Journal of Methodology, Springer, vol. 52(1), pages 695-709, December.
    2. Baba, Isa Abdullahi & Kaymakamzade, Bilgen & Hincal, Evren, 2018. "Two-strain epidemic model with two vaccinations," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 342-348.
    3. Tan, Yiping & Cai, Yongli & Wang, Xiaoqin & Peng, Zhihang & Wang, Kai & Yao, Ruoxia & Wang, Weiming, 2023. "Stochastic dynamics of an SIS epidemiological model with media coverage," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 204(C), pages 1-27.
    4. Yongli Cai & Xixi Wang & Weiming Wang & Min Zhao, 2013. "Stochastic Dynamics of an SIRS Epidemic Model with Ratio-Dependent Incidence Rate," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-11, June.
    5. Liu, Wenbin & Zheng, Qiben, 2015. "A stochastic SIS epidemic model incorporating media coverage in a two patch setting," Applied Mathematics and Computation, Elsevier, vol. 262(C), pages 160-168.
    6. Mao, Xuerong & Marion, Glenn & Renshaw, Eric, 2002. "Environmental Brownian noise suppresses explosions in population dynamics," Stochastic Processes and their Applications, Elsevier, vol. 97(1), pages 95-110, January.
    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. Tan, Yiping & Yao, Ruoxia, 2024. "Dynamics of an influenza epidemic model incorporating immune boosting and Ornstein–Uhlenbeck process," Chaos, Solitons & Fractals, Elsevier, vol. 188(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. Chen, Zhenwu & Xu, Zhiting, 2019. "A delayed diffusive influenza model with two-strain and two vaccinations," Applied Mathematics and Computation, Elsevier, vol. 349(C), pages 439-453.
    2. Baba, Isa Abdullahi & Abdulkadir, Rabiu Aliyu & Esmaili, Parvaneh, 2020. "Analysis of tuberculosis model with saturated incidence rate and optimal control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    3. Berrhazi, Badreddine & El Fatini, Mohamed & Lahrouz, Aadil & Settati, Adel & Taki, Regragui, 2018. "A stochastic SIRS epidemic model with a general awareness-induced incidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 968-980.
    4. Acuña-Zegarra, Manuel Adrian & Díaz-Infante, Saúl, 2018. "Stochastic asymptotic analysis of a multi-host model with vector transmission," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 510(C), pages 243-260.
    5. Farah, El Mehdi & Amine, Saida & Allali, Karam, 2021. "Dynamics of a time-delayed two-strain epidemic model with general incidence rates," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    6. Tong, Jinying & Zhang, Zhenzhong & Bao, Jianhai, 2013. "The stationary distribution of the facultative population model with a degenerate noise," Statistics & Probability Letters, Elsevier, vol. 83(2), pages 655-664.
    7. Huang, Zaitang & Cao, Junfei, 2018. "Ergodicity and bifurcations for stochastic logistic equation with non-Gaussian Lévy noise," Applied Mathematics and Computation, Elsevier, vol. 330(C), pages 1-10.
    8. Shi, Zhenfeng & Zhang, Xinhong & Jiang, Daqing, 2019. "Dynamics of an avian influenza model with half-saturated incidence," Applied Mathematics and Computation, Elsevier, vol. 355(C), pages 399-416.
    9. Liu, Meng & Wang, Ke, 2009. "Survival analysis of stochastic single-species population models in polluted environments," Ecological Modelling, Elsevier, vol. 220(9), pages 1347-1357.
    10. Qi, Kai & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed, 2021. "Virus dynamic behavior of a stochastic HIV/AIDS infection model including two kinds of target cell infections and CTL immune responses," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 188(C), pages 548-570.
    11. Dong, Qiuyue & Wang, Yan & Jiang, Daqing, 2025. "Dynamic analysis of an HIV model with CTL immune response and logarithmic Ornstein–Uhlenbeck process," Chaos, Solitons & Fractals, Elsevier, vol. 191(C).
    12. Liu, Qun & Jiang, Daqing & Shi, Ningzhong & Hayat, Tasawar & Ahmad, Bashir, 2017. "Stationary distribution and extinction of a stochastic SEIR epidemic model with standard incidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 476(C), pages 58-69.
    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. 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).
    15. Liu, Qun & Jiang, Daqing & Shi, Ningzhong & Hayat, Tasawar & Alsaedi, Ahmed, 2017. "Stationary distribution and extinction of a stochastic SIRS epidemic model with standard incidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 469(C), pages 510-517.
    16. Liu, Meng & Wang, Ke, 2013. "Dynamics and simulations of a logistic model with impulsive perturbations in a random environment," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 92(C), pages 53-75.
    17. Ji, Chunyan & Jiang, Daqing & Lei, Dongxia, 2019. "Dynamical behavior of a one predator and two independent preys system with stochastic perturbations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 649-664.
    18. 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).
    19. Wang, Kai & Fan, Hongjie & Zhu, Yanling, 2025. "Stationary distribution of a stochastic generalized SIRI epidemic model with reinfection and relapse," Statistics & Probability Letters, Elsevier, vol. 216(C).
    20. Das, Parthasakha & Das, Pritha & Mukherjee, Sayan, 2020. "Stochastic dynamics of Michaelis–Menten kinetics based tumor-immune interactions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 541(C).

    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:gam:jmathe:v:11:y:2023:i:7:p:1712-:d:1114863. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.