Stability of a general adaptive immunity virus dynamics model with multistages of infected cells and two routes of infection

2019 ◽  
Vol 43 (3) ◽  
pp. 1145-1175 ◽  
Author(s):  
Ahmed Elaiw ◽  
Noura AlShamrani
Keyword(s):  
Adaptive Immunity ◽  
Virus Dynamics ◽  
Dynamics Model ◽  
Infected Cells

scholarly journals Qualitative Analysis of a Generalized Virus Dynamics Model with Both Modes of Transmission and Distributed Delays

2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Khalid Hattaf ◽  
Noura Yousfi
Keyword(s):  
Qualitative Analysis ◽  
Distributed Delays ◽  
Virus Dynamics ◽  
Dynamics Model ◽  
Cell Infection ◽  
Modes Of Transmission ◽  
Proposed Model ◽  
Infection Models ◽  
Infected Cells ◽  
Incidence Functions

We propose a generalized virus dynamics model with distributed delays and both modes of transmission, one by virus-to-cell infection and the other by cell-to-cell transfer. In the proposed model, the distributed delays describe (i) the time needed for infected cells to produce new virions and (ii) the time necessary for the newly produced virions to become mature and infectious. In addition, the infection transmission process is modeled by general incidence functions for both modes. Furthermore, the qualitative analysis of the model is rigorously established and many known viral infection models with discrete and distributed delays are extended and improved.

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.

Impact of adaptive immune response and cellular infection on delayed virus dynamics with multi-stages of infected cells

2019 ◽  
Vol 13 (01) ◽  
pp. 2050003
Author(s):  
A. M. Elaiw ◽  
N. H. AlShamrani
Keyword(s):  
Immune Response ◽  
Immune Responses ◽  
Time Delays ◽  
Adaptive Immune Response ◽  
Virus Dynamics ◽  
Nonlinear Functions ◽  
Dynamics Model ◽  
Adaptive Immune ◽  
Infected Cells ◽  
Theoretical Results

In this investigation, we propose and analyze a virus dynamics model with multi-stages of infected cells. The model incorporates the effect of both humoral and cell-mediated immune responses. We consider two modes of transmissions, virus-to-cell and cell-to-cell. Multiple intracellular discrete-time delays have been integrated into the model. The incidence rate of infection as well as the generation and removal rates of all compartments are described by general nonlinear functions. We derive five threshold parameters which determine the existence of the equilibria of the model under consideration. A set of conditions on the general functions has been established which is sufficient to investigate the global stability of the five equilibria of the model. The global asymptotic stability of all equilibria is proven by utilizing Lyapunov function and LaSalle’s invariance principle. The theoretical results are illustrated by numerical simulations of the model with specific forms of the general functions.

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.

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