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Mathematical Analysis and Numerical Solution of a Model of HIV with a Discrete Time Delay

Author

Listed:
  • Abraham J. Arenas

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

  • Gilberto González-Parra

    (Department of Mathematics, New Mexico Institute of Mining and Technology, Socorro, NM 87801, USA)

  • Jhon J. Naranjo

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

  • Myladis Cogollo

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

  • Nicolás De La Espriella

    (Departamento de Física y Electrónica, Universidad de Córdoba, Montería 230002, Colombia)

Abstract

We propose a mathematical model based on a set of delay differential equations that describe intracellular HIV infection. The model includes three different subpopulations of cells and the HIV virus. The mathematical model is formulated in such a way that takes into account the time between viral entry into a target cell and the production of new virions. We study the local stability of the infection-free and endemic equilibrium states. Moreover, by using a suitable Lyapunov functional and the LaSalle invariant principle, it is proved that if the basic reproduction ratio is less than unity, the infection-free equilibrium is globally asymptotically stable. In addition, we designed a non-standard difference scheme that preserves some relevant properties of the continuous mathematical model.

Suggested Citation

  • Abraham J. Arenas & Gilberto González-Parra & Jhon J. Naranjo & Myladis Cogollo & Nicolás De La Espriella, 2021. "Mathematical Analysis and Numerical Solution of a Model of HIV with a Discrete Time Delay," Mathematics, MDPI, vol. 9(3), pages 1-21, January.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:3:p:257-:d:488520
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    References listed on IDEAS

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