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- Title
Mathematical Analysis and Numerical Solution of a Model of HIV with a Discrete Time Delay.
- Authors
Arenas, Abraham J.; González-Parra, Gilberto; Naranjo, Jhon J.; Cogollo, Myladis; De La Espriella, Nicolás; Rodríguez, Francisco
- 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.
- Subjects
NUMERICAL solutions to differential equations; MATHEMATICAL analysis; DELAY differential equations; HIV infections; MATHEMATICAL models; GLOBAL analysis (Mathematics)
- Publication
Mathematics (2227-7390), 2021, Vol 9, Issue 3, p257
- ISSN
2227-7390
- Publication type
Article
- DOI
10.3390/math9030257