Global stability analysis of humoral immunity virus dynamics model including latently 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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Global Properties of a General Latent Pathogen Dynamics Model with Delayed Pathogenic and Cellular Infections

Discrete Dynamics in Nature and Society ◽

10.1155/2019/9585497 ◽

2019 ◽

Vol 2019 ◽

pp. 1-18 ◽

Cited By ~ 18

Author(s):

A. M. Elaiw ◽

A. A. Almatrafi ◽

A. D. Hobiny ◽

K. Hattaf

Keyword(s):

Global Stability ◽

Infection Model ◽

Global Dynamics ◽

Dynamics Model ◽

Pathogen Dynamics ◽

Global Properties ◽

Latently Infected ◽

Infected Cells ◽

Theoretical Results ◽

Pathogenic Infection

This paper studies the global dynamics of a general pathogenic infection model with two ways of infections. The effect of antibody immune response is analyzed. We incorporate three discrete time delays and both latently infected cells and actively infected cells. The infection rate and production and clearance/death rates of the cells and pathogens are given by general functions. We determine two threshold parameters to investigate the global stability of three equilibria. We use Lyapunov method to establish the global stability. We support our theoretical results by numerical simulations.

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Global stability analysis of a general nonlinear scabies dynamics model

Chaos Solitons & Fractals ◽

10.1016/j.chaos.2020.110133 ◽

2020 ◽

Vol 138 ◽

pp. 110133

Author(s):

N.H. AlShamrani ◽

A.M. Elaiw ◽

H. Batarfi ◽

A.D. Hobiny ◽

H. Dutta

Keyword(s):

Stability Analysis ◽

Global Stability ◽

Dynamics Model ◽

Global Stability Analysis

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

Journal of Biological System ◽

10.1142/s0218339016500273 ◽

2016 ◽

Vol 24 (04) ◽

pp. 535-560 ◽

Cited By ~ 4

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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