scholarly journals Mathematical analysis of an age-structured HIV-1 infection model with CTL immune response

2019 ◽  
Vol 16 (6) ◽  
pp. 7850-7882
Author(s):  
Xiaohong Tian ◽  
◽  
Rui Xu ◽  
Jiazhe Lin ◽  
Keyword(s):  
Immune Response ◽  
Mathematical Analysis ◽  
Infection Model ◽  
Age Structured ◽  
Ctl Immune Response ◽  
Hiv 1

scholarly journals Global Dynamics of a Delayed HIV-1 Infection Model with CTL Immune Response

2011 ◽  
Vol 2011 ◽  
pp. 1-13 ◽  
Author(s):  
Yunfei Li ◽  
Rui Xu ◽  
Zhe Li ◽  
Shuxue Mao
Keyword(s):  
Immune Response ◽  
Viral Infection ◽  
Infection Model ◽  
Global Dynamics ◽  
Asymptotically Stable ◽  
Basic Reproduction Ratio ◽  
Globally Asymptotically Stable ◽  
Reproduction Ratio ◽  
Ctl Immune Response ◽  
Hiv 1

A delayed HIV-1 infection model with CTL immune response is investigated. By using suitable Lyapunov functionals, it is proved that the infection-free equilibrium is globally asymptotically stable if the basic reproduction ratio for viral infection is less than or equal to unity; if the basic reproduction ratio for CTL immune response is less than or equal to unity and the basic reproduction ratio for viral infection is greater than unity, the CTL-inactivated infection equilibrium is globally asymptotically stable; if the basic reproduction ratio for CTL immune response is greater than unity, the CTL-activated infection equilibrium is globally asymptotically stable.

scholarly journals Stability and Hopf Bifurcation in an HIV-1 Infection Model with Latently Infected Cells and Delayed Immune Response

2013 ◽  
Vol 2013 ◽  
pp. 1-12
Author(s):  
Haibin Wang ◽  
Rui Xu
Keyword(s):  
Immune Response ◽  
Infection Model ◽  
Asymptotically Stable ◽  
Basic Reproduction Ratio ◽  
Globally Asymptotically Stable ◽  
Reproduction Ratio ◽  
Latently Infected ◽  
Infected Cells ◽  
Ctl Immune Response ◽  
Hiv 1

An HIV-1 infection model with latently infected cells and delayed immune response is investigated. By analyzing the corresponding characteristic equations, the local stability of each of feasible equilibria is established and the existence of Hopf bifurcations at the CTL-activated infection equilibrium is also studied. By means of suitable Lyapunov functionals and LaSalle’s invariance principle, it is proved that the infection-free equilibrium is globally asymptotically stable if the basic reproduction ratio for viral infectionR0≤1; if the basic reproduction ratio for viral infectionR0>1and the basic reproduction ratio for CTL immune responseR1≤1, the CTL-inactivated infection equilibrium is globally asymptotically stable. If the basic reproduction ratio for CTL immune responseR1>1, the global stability of the CTL-activated infection equilibrium is also derived when the time delayτ=0. Numerical simulations are carried out to illustrate the main results.

scholarly journals Global Stability of HIV-1 Infection Model with Two Time Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Hui Miao ◽  
Xamxinur Abdurahman ◽  
Ahmadjan Muhammadhaji
Keyword(s):  
Immune Response ◽  
Delay Differential Equations ◽  
Time Delays ◽  
Infection Model ◽  
Global Dynamics ◽  
Response Model ◽  
Delay Differential ◽  
Ctl Immune Response ◽  
Hiv 1

We investigate global dynamics for a system of delay differential equations which describes a virus-immune interaction in vivo. The model has two time delays describing time needed for infection of cell and CTLs generation. Our model admits three possible equilibria: infection-free equilibrium, CTL-absent infection equilibrium, and CTL-present infection equilibrium. The effect of time delay on stability of the equilibria of the CTL immune response model has been studied.

Sign in / Sign up

Export Citation Format

Share Document