IDEAS home Printed from https://ideas.repec.org/a/wly/jnljam/v2018y2018i1n3420528.html

A Stochastic TB Model for a Crowded Environment

Author

Listed:
  • Sibaliwe Maku Vyambwera
  • Peter Witbooi

Abstract

We propose a stochastic compartmental model for the population dynamics of tuberculosis. The model is applicable to crowded environments such as for people in high density camps or in prisons. We start off with a known ordinary differential equation model, and we impose stochastic perturbation. We prove the existence and uniqueness of positive solutions of a stochastic model. We introduce an invariant generalizing the basic reproduction number and prove the stability of the disease‐free equilibrium when it is below unity or slightly higher than unity and the perturbation is small. Our main theorem implies that the stochastic perturbation enhances stability of the disease‐free equilibrium of the underlying deterministic model. Finally, we perform some simulations to illustrate the analytical findings and the utility of the model.

Suggested Citation

  • Sibaliwe Maku Vyambwera & Peter Witbooi, 2018. "A Stochastic TB Model for a Crowded Environment," Journal of Applied Mathematics, John Wiley & Sons, vol. 2018(1).
    • Handle: RePEc:wly:jnljam:v:2018:y:2018:i:1:n:3420528
    DOI: 10.1155/2018/3420528
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2018/3420528
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2018/3420528?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
    ---><---

    References listed on IDEAS

    as
    1. Liyan Wang & Huilin Huang & Ancha Xu & Weiming Wang, 2013. "Stochastic Extinction in an SIRS Epidemic Model Incorporating Media Coverage," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    2. Liyan Wang & Huilin Huang & Ancha Xu & Weiming Wang, 2013. "Stochastic Extinction in an SIRS Epidemic Model Incorporating Media Coverage," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-8, December.
    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. Ashenafi Kelemu Mengistu & Peter J. Witbooi, 2020. "Mathematical Analysis of TB Model with Vaccination and Saturated Incidence Rate," Abstract and Applied Analysis, John Wiley & Sons, vol. 2020(1).
    2. Sibaliwe Maku Vyambwera & Peter Witbooi, 2024. "Optimal Intervention Strategies on TB Epidemiology in a Prison Population," Abstract and Applied Analysis, John Wiley & Sons, vol. 2024(1).

    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. Lixia Zuo & Maoxing Liu, 2014. "Effect of Awareness Programs on the Epidemic Outbreaks with Time Delay," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    2. Feng Rao, 2014. "Dynamics Analysis of a Stochastic SIR Epidemic Model," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).

    More about this item

    Statistics

    Access and download statistics

    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:wly:jnljam:v:2018:y:2018:i:1:n:3420528. 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: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/4185 .

    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.