Dynamics of virus infection model with nonlytic immune response induced by stochastic noise

2017 ◽  
Vol 99 ◽  
pp. 124-132 ◽  
Author(s):  
Dongxi Li ◽  
Xiaowei Cui
Keyword(s):  
Immune Response ◽  
Virus Infection ◽  
Infection Model ◽  
Stochastic Noise ◽  
Virus Infection Model

A Delayed Virus Infection Model with Cell-to-Cell Transmission and CTL Immune Response

2017 ◽  
Vol 27 (10) ◽  
pp. 1750150 ◽  
Author(s):  
Yu Yang ◽  
Tonghua Zhang ◽  
Yancong Xu ◽  
Jinling Zhou
Keyword(s):  
Immune Response ◽  
Time Delay ◽  
Virus Infection ◽  
Multiple Time Scales ◽  
Infection Model ◽  
Multiple Time ◽  
Ctl Response ◽  
Cell Transmission ◽  
Ctl Immune Response ◽  
Virus Infection Model

In this paper, a delayed virus infection model with cell-to-cell transmission and CTL immune response is investigated. In the model, time delay is incorporated into the CTL response. By constructing Lyapunov functionals, global dynamical properties of the two boundary equilibria are established. Our results show that time delay in the CTL response process may lead to sustained oscillation. To further investigate the nature of the oscillation, we apply the method of multiple time scales to calculate the normal form on the center manifold of the model. At the end of the paper, numerical simulations are carried out, which support our theoretical results.

scholarly journals Global Dynamics of Virus Infection Model with Antibody Immune Response and Distributed Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
A. M. Elaiw ◽  
A. Alhejelan ◽  
M. A. Alghamdi
Keyword(s):  
Immune Response ◽  
Steady State ◽  
Virus Infection ◽  
Reproduction Number ◽  
Distributed Delays ◽  
Infection Model ◽  
Qualitative Behavior ◽  
Global Dynamics ◽  
Globally Asymptotically Stable ◽  
Virus Infection Model

We present qualitative behavior of virus infection model with antibody immune response. The incidence rate of infection is given by saturation functional response. Two types of distributed delays are incorporated into the model to account for the time delay between the time when uninfected cells are contacted by the virus particle and the time when emission of infectious (matures) virus particles. Using the method of Lyapunov functional, we have established that the global stability of the steady states of the model is determined by two threshold numbers, the basic reproduction numberR0and antibody immune response reproduction numberR1. We have proven that ifR0≤1, then the uninfected steady state is globally asymptotically stable (GAS), ifR1≤1<R0, then the infected steady state without antibody immune response is GAS, and ifR1>1, then the infected steady state with antibody immune response is GAS.

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