Stability analysis for viral infection model with multitarget cells, Beddington-DeAngelis functional response, and humoral immunity
type: Item
instance of: scholarly article
title: Stability analysis for viral infection model with multitarget cells, Beddington-DeAngelis functional response, and humoral immunity
zbMATH Open document ID: 1418.92078
DOI: 10.1155/2015/654507
author: Xinxin Tian
author: Jinliang Wang
published in: Discrete Dynamics in Nature and Society
publication date: 2019-02-19T00:00:00Z
review text: Summary: We formulate a \((2n+2)\)-dimensional viral infection model with humoral immunity, \(n\) classes of uninfected target cells and \(n\) classes of infected cells. The incidence rate of infection is given by nonlinear incidence rate, Beddington-DeAngelis functional response. The model admits discrete time delays describing the time needed for infection of uninfected target cells and virus replication. By constructing suitable Lyapunov functionals, we establish that the global dynamics are determined by two sharp threshold parameters: \(\mathfrak{R}_0\) and \(\mathfrak{R}_1\). Namely, a typical two-threshold scenario is shown. If \(\mathfrak{R}_0 \leq 1\), the infection-free equilibrium \(P_0\) is globally asymptotically stable, and the viruses are cleared. If \(\mathfrak{R}_1 \leq 1 < \mathfrak{R}_0\), the immune-free equilibrium \(P_1\) is globally asymptotically stable, and the infection becomes chronic but with no persistent antibody immune response. If \(\mathfrak{R}_1 > 1\), the endemic equilibrium \(P_2\) is globally asymptotically stable, and the infection is chronic with persistent antibody immune response.
Mathematics Subject Classification ID: 92C60
Mathematics Subject Classification ID: 92D30
Mathematics Subject Classification ID: 92C50
zbMATH DE Number: 7025442
Wikidata QID: Q59105326
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2015/654507
OpenAlex ID: W1481083378
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description: scientific article; zbMATH DE number 7025442