Stability of a general HIV-1 reaction–diffusion model with multiple delays and immune response

Ahmed M. Elaiw and Afnan D. Al Agha

Physica A: Statistical Mechanics and its Applications, 2019, vol. 536, issue C

Abstract: The aim of this paper is to study a general HIV-1 reaction–diffusion model with space-dependent diffusion coefficients and antibody immune response. The model contains four discrete time delays and three categories of infected cells: Latently infected cells, short-lived productively infected cells and long-lived productively infected cells. The effect of highly active antiretroviral therapies (HAART) used to treat HIV-1 is incorporated into the model. The existence, non-negativity and boundedness of solutions are studied in order to verify the well-posedness of the model. All possible equilibria of the model are evaluated and the threshold parameters needed for their existence and stability are investigated. The global asymptotic stability of the corresponding equilibria are proved by building suitable Lyapunov functionals. The numerical simulations are conducted in order to confirm the theoretical results and show the behavior of solutions in space and time.

Keywords: HIV dynamics; Diffusion; Immune response; Global stability; Time delay (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:536:y:2019:i:c:s0378437119314839

DOI: 10.1016/j.physa.2019.122593

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