Spatiotemporal dynamics of an HIV infection model with delay in immune response activation
type: Item
instance of: scholarly article
title: Spatiotemporal dynamics of an HIV infection model with delay in immune response activation
zbMATH Open document ID: 1487.92012
DOI: 10.1155/2018/3294268
author: Mehdi Maziane
author: Khalid Hattaf
author: Noura Yousfi
published in: International Journal of Differential Equations
publication date: 2018-08-10T00:00:00Z
review text: Summary: We propose and analyse a human immunodeficiency virus (HIV) infection model with spatial diffusion and delay in the immune response activation. In the proposed model, the immune response is presented by the cytotoxic T lymphocytes (CTL) cells. We first prove that the model is well-posed by showing the global existence, positivity, and boundedness of solutions. The model has three equilibria, namely, the free-infection equilibrium, the immune-free infection equilibrium, and the chronic infection equilibrium. The global stability of the first two equilibria is fully characterized by two threshold parameters that are the basic reproduction number \(R_0\) and the CTL immune response reproduction number \(R_1\). The stability of the last equilibrium depends on \(R_0\) and \(R_1\) as well as time delay \(\tau\) in the CTL activation. We prove that the chronic infection equilibrium is locally asymptotically stable when the time delay is sufficiently small, while it loses its stability and a Hopf bifurcation occurs when \(\tau\) passes through a certain critical value.
Mathematics Subject Classification ID: 92C60
Mathematics Subject Classification ID: 35M33
Mathematics Subject Classification ID: 35Q92
zbMATH DE Number: 6915951
zbMATH Keywords: human immunodeficiency virus (HIV) infection model
zbMATH Keywords: spatial diffusion
zbMATH Keywords: delay in immune response activation
zbMATH Keywords: global existence
zbMATH Keywords: positivity
zbMATH Keywords: boundedness
zbMATH Keywords: free-infection equilibrium
zbMATH Keywords: immune-free infection equilibrium
zbMATH Keywords: chronic infection equilibrium
zbMATH Keywords: global stability
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2018/3294268
OpenAlex ID: W2792619630
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Wikidata QID: Q130190411
description: scientific article; zbMATH DE number 6915951