Modeling inhibitory effect on the growth of uninfected T cells caused by infected T cells: stability and Hopf bifurcation
type: Item
instance of: scholarly article
title: Modeling inhibitory effect on the growth of uninfected T cells caused by infected T cells: stability and Hopf bifurcation
zbMATH Open document ID: 1431.92136
DOI: 10.1155/2018/3176893
author: Yahui Ji
author: Wanbiao Ma
author: Keying Song
published in: Computational \& Mathematical Methods in Medicine
publication date: 2019-07-09T00:00:00Z
review text: Summary: We consider a class of viral infection dynamic models with inhibitory effect on the growth of uninfected T cells caused by infected T cells and logistic target cell growth. The basic reproduction number \(R_0\) is derived. It is shown that the uninfected equilibrium is globally asymptotically stable if \(R_0 < 1\). Sufficient conditions for the existence of Hopf bifurcation at the infected equilibrium are investigated by analyzing the distribution of eigenvalues. Furthermore, the properties of Hopf bifurcation are determined by the normal form theory and the center manifold. Numerical simulations are carried out to support the theoretical analysis.
Mathematics Subject Classification ID: 92D30
Mathematics Subject Classification ID: 92C60
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34D23
zbMATH DE Number: 7077752
zbMATH Keywords: viral infection dynamic models
zbMATH Keywords: inhibitory effect
zbMATH Keywords: uninfected T cell growth
Wikidata QID: Q64954164
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2018/3176893
OpenAlex ID: W2886169771
cites work: Q4449282
cites work: Mathematical Analysis of HIV-1 Dynamics in Vivo
cites work: Q4238190
cites work: A diffusive HIV infection model with nonlocal delayed transmission
cites work: Dynamics of HIV infection of CD4\(^ +\) T cells
cites work: A delay-differential equation model of HIV infection of \(\text{CD}4^+\) T-cells
cites work: Mathematical analysis of the global dynamics of a model for HIV infection of CD4\(^{+}\) T cells
cites work: Dynamic behaviors of a delayed HIV model with stage-structure
cites work: Caspase-1-mediated pyroptosis of the predominance for driving \(\mathrm{CD}4^+\) T cells death: a nonlocal spatial mathematical model
cites work: Global behavior of delay differential equations model of HIV infection with apoptosis
cites work: A class of virus dynamic model with inhibitory effect on the growth of uninfected T cells caused by infected T cells and its stability analysis
cites work: Introduction to functional differential equations
cites work: Delay differential equations: with applications in population dynamics
cites work: Oscillatory viral dynamics in a delayed HIV pathogenesis model
cites work: GLOBAL ANALYSIS FOR A DELAYED SIV MODEL WITH DIRECT AND ENVIRONMENTAL TRANSMISSIONS
cites work: On the zeros of a third degree exponential polynomial with applications to a delayed model for the control of testosterone secretion
cites work: Q3930015
cites work: Delayed Feedback Control and Bifurcation Analysis in a Chaotic Chemostat System
cites work: Q4778449
cites work: Stability and Hopf bifurcation in a delayed HIV infection model with general incidence rate and immune impairment
cites work: Dynamical analysis of a stochastic SIS epidemic model with nonlinear incidence rate and double epidemic hypothesis
description: scientific article; zbMATH DE number 7077752