Global stability of a delayed humoral immunity virus dynamics model with nonlinear incidence and infected cells removal rates

2015 ◽  
Vol 5 (2) ◽  
pp. 381-393 ◽  
Author(s):  
A. M. Elaiw ◽  
N. H. AlShamrani
Keyword(s):  
Global Stability ◽  
Humoral Immunity ◽  
Virus Dynamics ◽  
Dynamics Model ◽  
Removal Rates ◽  
Nonlinear Incidence ◽  
Infected Cells

Global stability of a delayed virus dynamics model with multi-staged infected progression and humoral immunity

2016 ◽  
Vol 09 (04) ◽  
pp. 1650060
Author(s):  
A. M. Ełaiw ◽  
N. H. AlShamrani
Keyword(s):  
Global Stability ◽  
Humoral Immunity ◽  
Removal Rate ◽  
Infection Model ◽  
Target Cells ◽  
Virus Dynamics ◽  
Nonlinear Functions ◽  
Dynamics Model ◽  
Discrete Delays ◽  
Infected Cells

In this paper, we propose a nonlinear virus dynamics model that describes the interactions of the virus, uninfected target cells, multiple stages of infected cells and B cells and includes multiple discrete delays. We assume that the incidence rate of infection and removal rate of infected cells are given by general nonlinear functions. The model can be seen as a generalization of several humoral immunity viral infection model presented in the literature. We derive two threshold parameters and establish a set of conditions on the general functions which are sufficient to establish the existence and global stability of the three equilibria of the model. We study the global asymptotic stability of the equilibria by using Lyapunov method. We perform some numerical simulations for the model with specific forms of the general functions and show that the numerical results are consistent with the theoretical results.

GLOBAL STABILITY OF A GENERAL VIRUS DYNAMICS MODEL WITH MULTI-STAGED INFECTED PROGRESSION AND HUMORAL IMMUNITY

2016 ◽  
Vol 24 (04) ◽  
pp. 535-560 ◽  
Author(s):  
A. M. ELAIW ◽  
N. H. ALSHAMRANI
Keyword(s):  
Humoral Immunity ◽  
Lyapunov Functions ◽  
Dynamical Behavior ◽  
Target Cells ◽  
Global Dynamics ◽  
Virus Dynamics ◽  
Nonlinear Functions ◽  
Dynamics Model ◽  
Number Formula ◽  
Infected Cells

In this paper, we propose an [Formula: see text]-dimensional nonlinear virus dynamics model that describes the interactions of the virus, uninfected target cells, [Formula: see text]-stages of infected cells and B cells. We assume that the incidence rate of infection, the generation and removal rates of all compartments are given by general nonlinear functions. We derive two threshold parameters, the basic reproduction number, [Formula: see text] and the humoral immunity number, [Formula: see text] and establish a set of conditions on the general functions which are sufficient to determine the global dynamics of the model. Utilizing Lyapunov functions and LaSalle’s invariance principle, the global asymptotic stability of all steady states of the model is proved. Numerical simulations are conducted for specific forms of the general functions in order to illustrate the dynamical behavior.

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