IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v373y2020ics0096300319310136.html
   My bibliography  Save this article

Stationary distribution of a stochastic cholera model between communities linked by migration

Author

Listed:
  • Liu, Qun
  • Jiang, Daqing
  • Hayat, Tasawar
  • Alsaedi, Ahmed
  • Ahmad, Bashir

Abstract

In this paper, we develop and study a stochastic cholera model between communities linked by migration. Firstly, we show that there exists a unique global positive solution of the considered system with any positive initial value. Then by using the stochastic Lyapunov analysis method, we obtain sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the positive solutions to the model. Our result shows that the migration and the small white noise are not beneficial for eliminating cholera. Finally, some examples together with numerical simulations are introduced to support the theoretical result.

Suggested Citation

  • Liu, Qun & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed & Ahmad, Bashir, 2020. "Stationary distribution of a stochastic cholera model between communities linked by migration," Applied Mathematics and Computation, Elsevier, vol. 373(C).
    • Handle: RePEc:eee:apmaco:v:373:y:2020:i:c:s0096300319310136
    DOI: 10.1016/j.amc.2019.125021
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300319310136
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2019.125021?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. Lee, Hyojung & Lee, Sunmi & Lee, Chang Hyeong, 2016. "Stochastic methods for epidemic models: An application to the 2009 H1N1 influenza outbreak in Korea," Applied Mathematics and Computation, Elsevier, vol. 286(C), pages 232-249.
    3. Cai, Yongli & Jiao, Jianjun & Gui, Zhanji & Liu, Yuting & Wang, Weiming, 2018. "Environmental variability in a stochastic epidemic model," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 210-226.
    4. 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.
    5. Aaron A. King & Edward L. Ionides & Mercedes Pascual & Menno J. Bouma, 2008. "Inapparent infections and cholera dynamics," Nature, Nature, vol. 454(7206), pages 877-880, August.
    6. Berge, Tsanou & Bowong, Samuel & Lubuma, Jean M.-S., 2017. "Global stability of a two-patch cholera model with fast and slow transmissions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 133(C), pages 142-164.
    7. Zhang, Huisen & Cai, Yongli & Fu, Shengmao & Wang, Weiming, 2019. "Impact of the fear effect in a prey-predator model incorporating a prey refuge," Applied Mathematics and Computation, Elsevier, vol. 356(C), pages 328-337.
    8. Sasaki, S. & Suzuki, H. & Fujino, Y. & Kimura, Y. & Cheelo, M., 2009. "Impact of drainage networks on cholera outbreaks in Lusaka, Zambia," American Journal of Public Health, American Public Health Association, vol. 99(11), pages 1982-1987.
    9. Cai, Li-Ming & Modnak, Chairat & Wang, Jin, 2017. "An age-structured model for cholera control with vaccination," Applied Mathematics and Computation, Elsevier, vol. 299(C), pages 127-140.
    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. Nguiwa, Tchule & Kolaye, Gabriel Guilsou & Justin, Mibaile & Moussa, Djaouda & Betchewe, Gambo & Mohamadou, Alidou, 2021. "Dynamic study of SIAISQVR−B fractional-order cholera model with control strategies in Cameroon Far North Region," Chaos, Solitons & Fractals, Elsevier, vol. 144(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. Liu, Qun & Jiang, Daqing, 2020. "Stationary distribution of a stochastic cholera model with imperfect vaccination," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 550(C).
    2. Liu, Qun & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed & Ahmad, Bashir, 2020. "Threshold behavior in two types of stochastic three strains influenza virus models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 549(C).
    3. Tiancai Liao & Hengguo Yu & Chuanjun Dai & Min Zhao, 2019. "Impact of Cell Size Effect on Nutrient-Phytoplankton Dynamics," Complexity, Hindawi, vol. 2019, pages 1-23, November.
    4. Ran, Xue & Hu, Lin & Nie, Lin-Fei & Teng, Zhidong, 2021. "Effects of stochastic perturbation and vaccinated age on a vector-borne epidemic model with saturation incidence rate," Applied Mathematics and Computation, Elsevier, vol. 394(C).
    5. Liu, Qun & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed & Ahmad, Bashir, 2020. "A stochastic SIRS epidemic model with logistic growth and general nonlinear incidence rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 551(C).
    6. 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).
    7. Wang, Weiming & Cai, Yongli & Ding, Zuqin & Gui, Zhanji, 2018. "A stochastic differential equation SIS epidemic model incorporating Ornstein–Uhlenbeck process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 921-936.
    8. Wang, Lei & Wang, Kai & Jiang, Daqing & Hayat, Tasawar, 2018. "Nontrivial periodic solution for a stochastic brucellosis model with application to Xinjiang, China," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 510(C), pages 522-537.
    9. Yang, Bo, 2018. "A stochastic Feline immunodeficiency virus model with vertical transmission," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 448-458.
    10. Hoang Pham, 2022. "Mathematical Modeling the Time-Delay Interactions between Tumor Viruses and the Immune System with the Effects of Chemotherapy and Autoimmune Diseases," Mathematics, MDPI, vol. 10(5), pages 1-15, February.
    11. 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.
    12. Liu, Qun & Jiang, Daqing, 2020. "Threshold behavior in a stochastic SIR epidemic model with Logistic birth," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    13. 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.
    14. Lan, Guijie & Wei, Chunjin & Zhang, Shuwen, 2019. "Long time behaviors of single-species population models with psychological effect and impulsive toxicant in polluted environments," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 828-842.
    15. Zhou, Baoquan & Jiang, Daqing & Han, Bingtao & Hayat, Tasawar, 2022. "Threshold dynamics and density function of a stochastic epidemic model with media coverage and mean-reverting Ornstein–Uhlenbeck process," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 196(C), pages 15-44.
    16. Cai, Yongli & Ding, Zuqin & Yang, Bin & Peng, Zhihang & Wang, Weiming, 2019. "Transmission dynamics of Zika virus with spatial structure—A case study in Rio de Janeiro, Brazil," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 729-740.
    17. Liu, Qun & Jiang, Daqing & He, Xiuli & Hayat, Tasawar & Alsaedi, Ahmed, 2019. "Stationary distribution of a stochastic predator–prey model with distributed delay and general functional response," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 513(C), pages 273-287.
    18. Tuerxun, Nafeisha & Wen, Buyu & Teng, Zhidong, 2021. "The stationary distribution in a class of stochastic SIRS epidemic models with non-monotonic incidence and degenerate diffusion," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 888-912.
    19. Nian, Fuzhong & Yao, Shuanglong, 2018. "The epidemic spreading on the multi-relationships network," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 866-873.
    20. Zhou, Baoquan & Han, Bingtao & Jiang, Daqing, 2021. "Ergodic property, extinction and density function of a stochastic SIR epidemic model with nonlinear incidence and general stochastic perturbations," Chaos, Solitons & Fractals, Elsevier, vol. 152(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:eee:apmaco:v:373:y:2020:i:c:s0096300319310136. 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.