Global stability of a virus dynamics model with Beddington–DeAngelis incidence rate and CTL immune response

2011 ◽  
Vol 66 (4) ◽  
pp. 825-830 ◽  
Author(s):  
Xia Wang ◽  
Youde Tao ◽  
Xinyu Song
Keyword(s):  
Immune Response ◽  
Global Stability ◽  
Incidence Rate ◽  
Virus Dynamics ◽  
Dynamics Model ◽  
Ctl Immune Response

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

scholarly journals Global Stability of Delayed Viral Infection Models with Nonlinear Antibody and CTL Immune Responses and General Incidence Rate

2016 ◽  
Vol 2016 ◽  
pp. 1-21 ◽  
Author(s):  
Hui Miao ◽  
Zhidong Teng ◽  
Zhiming Li
Keyword(s):  
Immune Response ◽  
Immune Responses ◽  
Antibody Response ◽  
Viral Infection ◽  
Global Stability ◽  
Incidence Rate ◽  
Cytotoxic T Lymphocyte ◽  
Dynamical Behavior ◽  
Infection Model ◽  
Ctl Immune Response

The dynamical behaviors for a five-dimensional viral infection model with three delays which describes the interactions of antibody, cytotoxic T-lymphocyte (CTL) immune responses, and nonlinear incidence rate are investigated. The threshold values for viral infection, antibody response, CTL immune response, CTL immune competition, and antibody competition, respectively, are established. Under certain assumptions, the threshold value conditions on the global stability of the infection-free, immune-free, antibody response, CTL immune response, and interior equilibria are proved by using the Lyapunov functionals method, respectively. Immune delay as a bifurcation parameter is further investigated. The numerical simulations are performed in order to illustrate the dynamical behavior of the model.

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