IDEAS home Printed from https://ideas.repec.org/a/hin/jnljam/2439520.html
   My bibliography  Save this article

A Stochastic Model for Malaria Transmission Dynamics

Author

Listed:
  • Rachel Waema Mbogo
  • Livingstone S. Luboobi
  • John W. Odhiambo

Abstract

Malaria is one of the three most dangerous infectious diseases worldwide (along with HIV/AIDS and tuberculosis). In this paper we compare the disease dynamics of the deterministic and stochastic models in order to determine the effect of randomness in malaria transmission dynamics. Relationships between the basic reproduction number for malaria transmission dynamics between humans and mosquitoes and the extinction thresholds of corresponding continuous-time Markov chain models are derived under certain assumptions. The stochastic model is formulated using the continuous-time discrete state Galton-Watson branching process (CTDSGWbp). The reproduction number of deterministic models is an essential quantity to predict whether an epidemic will spread or die out. Thresholds for disease extinction from stochastic models contribute crucial knowledge on disease control and elimination and mitigation of infectious diseases. Analytical and numerical results show some significant differences in model predictions between the stochastic and deterministic models. In particular, we find that malaria outbreak is more likely if the disease is introduced by infected mosquitoes as opposed to infected humans. These insights demonstrate the importance of a policy or intervention focusing on controlling the infected mosquito population if the control of malaria is to be realized.

Suggested Citation

  • Rachel Waema Mbogo & Livingstone S. Luboobi & John W. Odhiambo, 2018. "A Stochastic Model for Malaria Transmission Dynamics," Journal of Applied Mathematics, Hindawi, vol. 2018, pages 1-13, February.
    • Handle: RePEc:hin:jnljam:2439520
    DOI: 10.1155/2018/2439520
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/JAM/2018/2439520.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/JAM/2018/2439520.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2018/2439520?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
    ---><---

    Citations

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


    Cited by:

    1. Rehman, Attiq ul & Singh, Ram & Singh, Jagdev, 2022. "Mathematical analysis of multi-compartmental malaria transmission model with reinfection," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    2. Ghosh, M. & Olaniyi, S. & Obabiyi, O.S., 2020. "Mathematical analysis of reinfection and relapse in malaria dynamics," Applied Mathematics and Computation, Elsevier, vol. 373(C).
    3. Wang, Lei & Teng, Zhidong & Ji, Chunyan & Feng, Xiaomei & Wang, Kai, 2019. "Dynamical behaviors of a stochastic malaria model: A case study for Yunnan, China," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 435-454.

    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:hin:jnljam:2439520. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.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.