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Analysis of Within-Host Mathematical Models of Toxoplasmosis That Consider Time Delays

Author

Listed:
  • Sharmin Sultana

    (Department of Mathematics, New Mexico Tech, Socorro, NM 87801, USA)

  • Gilberto González-Parra

    (Department of Mathematics, New Mexico Tech, Socorro, NM 87801, USA
    Instituto de Matemática Multidisciplinar, Universitat Politècnica de València, 46022 Valencia, Spain)

  • Abraham J. Arenas

    (Departamento de Matemáticas y Estadística, Universidad de Córdoba, Monteria 230002, Colombia)

Abstract

In this paper, we investigate two within-host mathematical models that are based on differential equations. These mathematical models include healthy cells, tachyzoites, and bradyzoites. The first model is based on ordinary differential equations and the second one includes a discrete time delay. We found the models’ steady states and computed the basic reproduction number R 0 . Two equilibrium points exist in both models: the first is the disease-free equilibrium point and the second one is the endemic equilibrium point. We found that the initial quantity of uninfected cells has an impact on the basic reproduction number R 0 . This threshold parameter also depends on the contact rate between tachyzoites and uninfected cells, the contact rate between encysted bradyzoite and the uninfected cells, the conversion rate from tachyzoites to bradyzoites, and the death rate of the bradyzoites- and tachyzoites-infected cells. We investigated the local and global stability of the two equilibrium points for the within-host models that are based on differential equations. We perform numerical simulations to validate our analytical findings. We also demonstrated that the disease-free equilibrium point cannot lose stability regardless of the value of the time delay. The numerical simulations corroborated our analytical results.

Suggested Citation

  • Sharmin Sultana & Gilberto González-Parra & Abraham J. Arenas, 2023. "Analysis of Within-Host Mathematical Models of Toxoplasmosis That Consider Time Delays," Mathematics, MDPI, vol. 11(21), pages 1-24, October.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:21:p:4469-:d:1269380
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    References listed on IDEAS

    as
    1. Vargas-De-León, Cruz, 2011. "On the global stability of SIS, SIR and SIRS epidemic models with standard incidence," Chaos, Solitons & Fractals, Elsevier, vol. 44(12), pages 1106-1110.
    2. 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.
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