scholarly journals Virus dynamics model with intracellular delays and immune response

2015 ◽  
Vol 12 (1) ◽  
pp. 185-208 ◽  
Author(s):  
Haitao Song ◽  
◽  
Weihua Jiang ◽  
Shengqiang Liu ◽  
Keyword(s):  
Immune Response ◽  
Virus Dynamics ◽  
Dynamics Model ◽  
Intracellular Delays

Dynamical Analysis of Multipathways and Multidelays of General Virus Dynamics Model

2019 ◽  
Vol 29 (03) ◽  
pp. 1950031 ◽  
Author(s):  
Ángel G. Cervantes-Pérez ◽  
Eric Ávila-Vales
Keyword(s):  
Immune Response ◽  
Time Delays ◽  
Reproduction Number ◽  
Dynamical Analysis ◽  
Multiple Time Scales ◽  
Threshold Dynamics ◽  
Positive Equilibrium ◽  
Virus Dynamics ◽  
Multiple Time ◽  
Dynamics Model

This paper considers a general virus dynamics model with cell-mediated immune response and direct cell-to-cell infection modes. The model incorporates two types of intracellular distributed time delays and a discrete delay in the CTL immune response. Under certain conditions, the model exhibits a global threshold dynamics with respect to two parameters: the basic reproduction number and the reproduction number of immune response. We use suitable Lyapunov functionals and apply Lasalle’s invariance principle to establish the global asymptotic stability of the two boundary equilibria. We also perform a bifurcation analysis for the positive equilibrium to show that the time delays may lead to sustained oscillations. To determine the direction of the Hopf bifurcation and the stability of the periodic solutions, the method of multiple time scales is applied. Finally, we carry out numerical simulations to illustrate our results.

LYAPUNOV FUNCTION AND GLOBAL PROPERTIES OF VIRUS DYNAMICS WITH CTL IMMUNE RESPONSE

2008 ◽  
Vol 01 (04) ◽  
pp. 443-448 ◽  
Author(s):  
XIA WANG ◽  
YOUDE TAO
Keyword(s):  
Immune Response ◽  
Lyapunov Function ◽  
Lyapunov Functions ◽  
Disease Model ◽  
Virus Dynamics ◽  
Dynamics Model ◽  
Global Properties ◽  
The Stability ◽  
Ctl Immune Response

The stability of infections disease model with CTL immune response in vivo is considered in this paper. Explicit Lyapunov functions for our dynamics model with CTL immune response with nonlinear incidence of the form βVqTpfor the case q ≤ 1 are introduced, and global properties of the model are thereby established.

Dynamical behavior of a virus dynamics model with CTL immune response

2009 ◽  
Vol 213 (2) ◽  
pp. 329-347 ◽  
Author(s):  
Xueyong Zhou ◽  
Xiangyun Shi ◽  
Zhonghua Zhang ◽  
Xinyu Song
Keyword(s):  
Immune Response ◽  
Dynamical Behavior ◽  
Virus Dynamics ◽  
Dynamics Model ◽  
Ctl Immune Response

Impact of adaptive immune response and cellular infection on delayed virus dynamics with multi-stages of infected cells

2019 ◽  
Vol 13 (01) ◽  
pp. 2050003
Author(s):  
A. M. Elaiw ◽  
N. H. AlShamrani
Keyword(s):  
Immune Response ◽  
Immune Responses ◽  
Time Delays ◽  
Adaptive Immune Response ◽  
Virus Dynamics ◽  
Nonlinear Functions ◽  
Dynamics Model ◽  
Adaptive Immune ◽  
Infected Cells ◽  
Theoretical Results

In this investigation, we propose and analyze a virus dynamics model with multi-stages of infected cells. The model incorporates the effect of both humoral and cell-mediated immune responses. We consider two modes of transmissions, virus-to-cell and cell-to-cell. Multiple intracellular discrete-time delays have been integrated into the model. The incidence rate of infection as well as the generation and removal rates of all compartments are described by general nonlinear functions. We derive five threshold parameters which determine the existence of the equilibria of the model under consideration. A set of conditions on the general functions has been established which is sufficient to investigate the global stability of the five equilibria of the model. The global asymptotic stability of all equilibria is proven by utilizing Lyapunov function and LaSalle’s invariance principle. The theoretical results are illustrated by numerical simulations of the model with specific forms of the general functions.

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