A Primary Infection Model for HIV and Immune response with Two Discrete Time Delays

2010 ◽  
Vol 18 (4) ◽  
pp. 385-399 ◽  
Author(s):  
Prashant K. Srivastava ◽  
M. Banerjee ◽  
Peeyush Chandra
Keyword(s):  
Immune Response ◽  
Discrete Time ◽  
Primary Infection ◽  
Time Delays ◽  
Infection Model

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.

scholarly journals Dynamic Consistent NSFD Scheme for a Delayed Viral Infection Model with Immune Response and Nonlinear Incidence

2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Jinhu Xu ◽  
Yan Geng
Keyword(s):  
Immune Response ◽  
Viral Infection ◽  
Discrete Time ◽  
Discrete Model ◽  
Continuous Model ◽  
Infection Model ◽  
Time Step ◽  
Nonlinear Incidence ◽  
Nsfd Scheme ◽  
Viral Infection Model

In this paper, a discrete-time model has been proposed by applying nonstandard finite difference (NSFD) scheme to solve a delayed viral infection model with immune response and general nonlinear incidence. It is shown that the discrete model has equilibria which are exactly the same as those of the original continuous model. Using discrete-time analogue of Lyapunov functionals, the global asymptotic stability of the equilibria of the discrete model is fully determined by the basic reproduction number of the virus and immune response, R0 and R1, with no restriction on the time step size, which implies that the NSFD scheme preserves the qualitative dynamics of the corresponding continuous model.

Synchronization for discrete-time complex networks with probabilistic time delays

2019 ◽  
Vol 525 ◽  
pp. 1088-1101 ◽  
Author(s):  
Ranran Cheng ◽  
Mingshu Peng ◽  
Jinchen Yu ◽  
Haifen Li
Keyword(s):  
Complex Networks ◽  
Discrete Time ◽  
Time Delays
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