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

Abraham J. Arenas, Gilberto González-Parra, Jhon J. Naranjo, Myladis Cogollo and Nicolás De La Espriella
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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

Mathematics, 2021, vol. 9, issue 3, 1-21

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.

Keywords: HIV infection; mathematical delay model; eclipse phase; NSFD; numerical simulation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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