IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i3p354-d732216.html
   My bibliography  Save this article

Mathematical Modeling of Toxoplasmosis Considering a Time Delay in the Infectivity of Oocysts

Author

Listed:
  • Gilberto González-Parra

    (Department of Mathematics, New Mexico Tech, New Mexico Institute of Mining and Technology, Socorro, NM 87801, USA
    These authors contributed equally to this work.)

  • Sharmin Sultana

    (Department of Mathematics, New Mexico Tech, New Mexico Institute of Mining and Technology, Socorro, NM 87801, USA
    These authors contributed equally to this work.)

  • Abraham J. Arenas

    (Departamento de Matematicas y Estadistica, Universidad de Cordoba, Monteria 230002, Colombia
    These authors contributed equally to this work.)

Abstract

In this paper, we study the effect of the introduction of a time delay on the dynamics of toxoplasmosis. This time delay is the elapsed time from when oocysts become present in the environment and when they become infectious. We construct a mathematical model that includes cats and oocysts in the environment. We include the effect of oocysts, since they are crucial for the dynamics of toxoplasmosis. The likelihood of the acquisition of Toxoplasma gondii infection depends on the environmental load of the parasite. Furthermore, the model considers the possibility of vaccination of the feline host. In the mathematical model, we consider directly the infection of cats through the oocysts shed by other cats. We prove that the basic reproduction number R 0 is a secondary parameter that determines the global dynamics of toxoplasmosis in cat populations. We study the effect of the time delay on the stability of the steady states. We find that the time delay cannot change the stability of the endemic state, which is an important result from the biological point of view. Numerical simulations are performed to support the theoretical results and obtain further insight into understanding toxoplasmosis dynamics in cat populations.

Suggested Citation

  • Gilberto González-Parra & Sharmin Sultana & Abraham J. Arenas, 2022. "Mathematical Modeling of Toxoplasmosis Considering a Time Delay in the Infectivity of Oocysts," Mathematics, MDPI, vol. 10(3), pages 1-20, January.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:3:p:354-:d:732216
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/3/354/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/3/354/
    Download Restriction: no
    ---><---

    Citations

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


    Cited by:

    1. Vsevolod G. Sorokin & Andrei V. Vyazmin, 2022. "Nonlinear Reaction–Diffusion Equations with Delay: Partial Survey, Exact Solutions, Test Problems, and Numerical Integration," Mathematics, MDPI, vol. 10(11), pages 1-39, May.
    2. Sharmin Sultana & Gilberto González-Parra & Abraham J. Arenas, 2023. "Mathematical Modeling of Toxoplasmosis in Cats with Two Time Delays under Environmental Effects," Mathematics, MDPI, vol. 11(16), pages 1-20, August.
    3. Andrei D. Polyanin & Vsevolod G. Sorokin, 2023. "Exact Solutions of Reaction–Diffusion PDEs with Anisotropic Time Delay," Mathematics, MDPI, vol. 11(14), pages 1-19, July.
    4. Sharmin Sultana & Gilberto González-Parra & Abraham J. Arenas, 2023. "A Generalized Mathematical Model of Toxoplasmosis with an Intermediate Host and the Definitive Cat Host," Mathematics, MDPI, vol. 11(7), pages 1-17, March.
    5. Andrei D. Polyanin & Vsevolod G. Sorokin, 2023. "Reductions and Exact Solutions of Nonlinear Wave-Type PDEs with Proportional and More Complex Delays," Mathematics, MDPI, vol. 11(3), pages 1-25, January.

    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:10:y:2022:i:3:p:354-:d:732216. 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: 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.