scholarly journals Global Properties of Latent Virus Dynamics Models with Immune Impairment and Two Routes of Infection

2019 ◽  
Vol 8 (2) ◽  
pp. 16
Author(s):  
Aeshah A. Raezah ◽  
Ahmed M. Elaiw ◽  
Badria S. Alofi
Keyword(s):  
Global Stability ◽  
Lyapunov Method ◽  
Incidence Rates ◽  
Steady States ◽  
Global Properties ◽  
Infection Models ◽  
Latently Infected ◽  
Immune Impairment ◽  
Infected Cells ◽  
Dynamics Models

This paper studies the global stability of viral infection models with CTL immune impairment. We incorporate both productively and latently infected cells. The models integrate two routes of transmission, cell-to-cell and virus-to-cell. In the second model, saturated virus–cell and cell–cell incidence rates are considered. The basic reproduction number is derived and two steady states are calculated. We first establish the nonnegativity and boundedness of the solutions of the system, then we investigate the global stability of the steady states. We utilize the Lyapunov method to prove the global stability of the two steady states. We support our theorems by numerical simulations.

scholarly journals Stability of discrete-time HIV dynamics models with three categories of infected CD4+ T-cells

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
A. M. Elaiw ◽  
M. A. Alshaikh
Keyword(s):  
Global Stability ◽  
Discrete Time ◽  
Nonlinear Functions ◽  
Hiv Dynamics ◽  
Nonstandard Finite Difference Scheme ◽  
Infection Models ◽  
Latently Infected ◽  
Infected Cells ◽  
Dynamics Models ◽  
Theoretical Results

Abstract This paper studies the global stability of two discrete-time HIV infection models. The models integrate (i) latently infected cells, (ii) long-lived chronically infected cells and (iii) short-lived infected cells. The second model generalizes the first one by assuming that the incidence rate of infection as well as the production and removal rates of the HIV particles and cells are modeled by general nonlinear functions. We discretize the continuous-time models by using a nonstandard finite difference scheme. The positivity and boundedness of solutions are established. The basic reproduction number is derived. By using the Lyapunov method, we prove the global stability of the models. Numerical simulations are presented to illustrate our theoretical results.

scholarly journals Global Properties of a General Latent Pathogen Dynamics Model with Delayed Pathogenic and Cellular Infections

2019 ◽  
Vol 2019 ◽  
pp. 1-18 ◽  
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.

Analysis of within-host CHIKV dynamics models with general incidence rate

2018 ◽  
Vol 11 (05) ◽  
pp. 1850062 ◽  
Author(s):  
Ahmed M. Elaiw ◽  
Taofeek O. Alade ◽  
Saud M. Alsulami
Keyword(s):  
Global Stability ◽  
Incidence Rate ◽  
Sufficient Conditions ◽  
Nonlinear Function ◽  
Steady States ◽  
Positive Steady States ◽  
Latently Infected ◽  
The Stability ◽  
Dynamics Models ◽  
Theoretical Results

In this paper we study the stability analysis of two within-host Chikungunya virus (CHIKV) dynamics models. The incidence rate between the CHIKV and the uninfected monocytes is modeled by a general nonlinear function. The second model considers two types of infected monocytes (i) latently infected monocytes which do not generate CHIKV and (ii) actively infected monocytes which produce the CHIKV particles. Sufficient conditions are found which guarantee the global stability of the positive steady states. Using the Lyapunov function, we established the global stability of the steady states of the models. The theoretical results are confirmed by numerical simulations.

scholarly journals Global Stability of Humoral Immunity HIV Infection Models with Chronically Infected Cells and Discrete Delays

2015 ◽  
Vol 2015 ◽  
pp. 1-25
Author(s):  
A. M. Elaiw ◽  
N. A. Alghamdi
Keyword(s):  
Hiv Infection ◽  
Global Stability ◽  
Incidence Rate ◽  
Sufficient Conditions ◽  
Humoral Immune ◽  
Infection Models ◽  
Existence And Stability ◽  
Discrete Delays ◽  
Infected Cells ◽  
Theoretical Results

We study the global stability of three HIV infection models with humoral immune response. We consider two types of infected cells: the first type is the short-lived infected cells and the second one is the long-lived chronically infected cells. In the three HIV infection models, we modeled the incidence rate by bilinear, saturation, and general forms. The models take into account two types of discrete-time delays to describe the time between the virus entering into an uninfected CD4+T cell and the emission of new active viruses. The existence and stability of all equilibria are completely established by two bifurcation parameters,R0andR1. The global asymptotic stability of the steady states has been proven using Lyapunov method. In case of the general incidence rate, we have presented a set of sufficient conditions which guarantee the global stability of model. We have presented an example and performed numerical simulations to confirm our theoretical results.

GLOBAL PROPERTIES OF HIV DYNAMICS MODELS INCLUDING IMPAIRMENT OF B-CELL FUNCTIONS

2020 ◽  
Vol 28 (01) ◽  
pp. 1-25
Author(s):  
A. M. Elaiw ◽  
S. F. ALSHEHAIWEEN ◽  
A. D. HOBINY
Keyword(s):  
B Cell ◽  
Antiviral Treatment ◽  
Drug Efficacy ◽  
Cell Functions ◽  
Hiv Dynamics ◽  
Proposed Model ◽  
Latently Infected ◽  
Number Formula ◽  
Infected Cells ◽  
Dynamics Models

In this paper, we develop mathematical models that include impairment of B-cell functions in order to study HIV dynamics. Two forms of the incidence rate have been considered, bilinear and general nonlinear. Three types of infected cells have been incorporated into the models, namely latently infected, short-lived productively infected and long-lived productively infected. The models have at most two equilibria, whose existence is characterized by means of the basic reproduction number [Formula: see text]. The global stability of each equilibrium is proven by using the Lyapunov method. The effects of impairment of B-cell functions and of antiviral treatment on the human immunodeficiency virus (HIV) dynamics are studied. We have shown that if the functions of B-cell are impaired, then the concentration of HIV increases in the plasma. Moreover, we have determined the minimal drug efficacy which is required to reduce the concentration of HIV particles to a lower level. We have shown that a more accurate computation of drug efficacy can be performed by using our proposed model. Our theoretical results are illustrated by means of numerical simulations.

scholarly journals Global properties of saturated chikungunya virus dynamics models with cellular infection and delays

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
A. M. Elaiw ◽  
S. E. Almalki ◽  
A. D. Hobiny
Keyword(s):  
Time Delay ◽  
Chikungunya Virus ◽  
Mass Action ◽  
Virus Dynamics ◽  
Maturation Time ◽  
Chikv Infection ◽  
Global Properties ◽  
Latently Infected ◽  
Dynamics Models ◽  
Theoretical Results

AbstractThis paper studies the global properties of chikungunya virus (CHIKV) dynamics models with both CHIKV-to-monocytes and infected-to-monocyte transmissions. We assume that the infection rate of modeling CHIKV infection is given by saturated mass action. The effect of antibody immune response on the virus dynamics is modeled. The models included three types of time delays, discrete or distributed. The first type of delay is the time between CHIKV entry an uninfected monocyte to be latently infected monocyte. The second time delay is the time between CHIKV entry an uninfected monocyte and the emission of immature CHIKV. The third time delay represents the CHIKV’s maturation time. Lyapunov method is utilized and LaSalle’s invariance principle is applied to address the global stability of equilibria. The model is numerically simulated to support theoretical results.

scholarly journals Stability of a Discrete-Time Pathogen Infection Model with Adaptive Immune Response

2020 ◽  
Vol 2020 ◽  
pp. 1-26
Author(s):  
M. A. Alshaikh ◽  
A. M. Elaiw
Keyword(s):  
Global Stability ◽  
Discrete Time ◽  
Adaptive Immune Response ◽  
Steady States ◽  
Infection Model ◽  
Continuous Time Model ◽  
Time Model ◽  
Adaptive Immune ◽  
Existence And Stability ◽  
Infected Cells

This paper studies the global stability of a discrete-time pathogen dynamic model with both cell-mediated and antibody immune responses. Both latently and actively infected cells are incorporated into the model. We discretize the continuous-time model by using the nonstandard finite difference (NSFD) method. We establish that NSFD preserves the nonnegativity and boundedness of the solutions of the model. We derive four threshold parameters which govern the existence and stability of the steady states. We establish by using the Lyapunov method, the global stability of the five steady states of the model. We illustrate our theoretical results by using numerical simulations.

scholarly journals Stability of discrete-time delayed pathogen infection models with latently infected cells

AIP Advances ◽  
2019 ◽  
Vol 9 (4) ◽  
pp. 045015
Author(s):  
A. M. Elaiw ◽  
M. A. Alshaikh
Keyword(s):  
Discrete Time ◽  
Pathogen Infection ◽  
Infection Models ◽  
Latently Infected ◽  
Infected Cells

Global dynamics of a class of HIV-1 infection models with latently infected cells

2015 ◽  
Vol 20 (1) ◽  
pp. 21-37 ◽  
Author(s):  
Haibin Wang ◽  
◽  
Rui Xu ◽  
Zhaowei Wang ◽  
Hui Chen
Keyword(s):  
Global Dynamics ◽  
Infection Models ◽  
Latently Infected ◽  
Infected Cells ◽  
Hiv 1
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