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.

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 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 stability of a fractional order HIV infection model with cure of infected cells in eclipse stage

2019 ◽  
Vol Volume 30 - 2019 - MADEV... ◽  
Author(s):  
Moussa Bachraoui ◽  
Khalid Hattaf ◽  
Noura Yousfi
Keyword(s):  
Hiv Infection ◽  
Global Stability ◽  
Fractional Order ◽  
Infection Model ◽  
Proposed Model ◽  
Immunodeficiency Virus ◽  
Infected Cells ◽  
Hiv Infection Model ◽  
With Memory ◽  
Theoretical Results

Modeling by fractional order differential equations has more advantages to describe the dynamics of phenomena with memory which exists in many biological systems. In this paper, we propose a fractional order model for human immunodeficiency virus (HIV) infection by including a class of infected cells that are not yet producing virus, i.e., cells in the eclipse stage. We first prove the positivity and bound-edness of solutions in order to ensure the well-posedness of the proposed model. By constructing appropriate Lyapunov functionals, the global stability of the disease-free equilibrium and the chronic infection equilibrium is established. Numerical simulations are presented in order to validate our theoretical results.

scholarly journals Asymptotic Stability of Caputo Type Fractional Neutral Dynamical Systems with Multiple Discrete Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Hai Zhang ◽  
Daiyong Wu ◽  
Jinde Cao
Keyword(s):  
Asymptotic Stability ◽  
Matrix Theory ◽  
Sufficient Conditions ◽  
Algebraic Approach ◽  
Stability Criteria ◽  
Differential Systems ◽  
Discrete Delays ◽  
Transcendental Equations ◽  
The Stability ◽  
Theoretical Results

We discuss the delay-independent asymptotic stability of Caputo type fractional-order neutral differential systems with multiple discrete delays. Based on the algebraic approach and matrix theory, the sufficient conditions are derived to ensure the asymptotic stability for all time-delay parameters. By applying the stability criteria, one can avoid solving the roots of transcendental equations. The results obtained are computationally flexible and convenient. Moreover, an example is provided to illustrate the effectiveness and applicability of the proposed theoretical results.

scholarly journals Stability of a CTL-mediated immunity HIV infection models with silent infected cells and cellular infection

2020 ◽  
Vol 22 (03) ◽  
pp. 216-237
Author(s):  
Noura H. AlShamrani ◽  
Ahmed M. Elaiw
Keyword(s):  
Hiv Infection ◽  
Infection Models ◽  
Infected Cells

scholarly journals Analysis of an HTLV/HIV dual infection model with diffusion

2021 ◽  
Vol 18 (6) ◽  
pp. 9430-9473
Author(s):  
A. M. Elaiw ◽  
◽  
N. H. AlShamrani ◽  
◽  
Keyword(s):  
Lyapunov Functions ◽  
Global Solutions ◽  
Dual Infection ◽  
Steady States ◽  
Infection Model ◽  
Well Posedness ◽  
Pde Model ◽  
Existence And Stability ◽  
Infected Cells ◽  
Theoretical Results

<abstract><p>In the literature, several HTLV-I and HIV single infections models with spatial dependence have been developed and analyzed. However, modeling HTLV/HIV dual infection with diffusion has not been studied. In this work we derive and investigate a PDE model that describes the dynamics of HTLV/HIV dual infection taking into account the mobility of viruses and cells. The model includes the effect of Cytotoxic T lymphocytes (CTLs) immunity. Although HTLV-I and HIV primarily target the same host, CD$ 4^{+} $T cells, via infected-to-cell (ITC) contact, however the HIV can also be transmitted through free-to-cell (FTC) contact. Moreover, HTLV-I has a vertical transmission through mitosis of active HTLV-infected cells. The well-posedness of solutions, including the existence of global solutions and the boundedness, is justified. We derive eight threshold parameters which govern the existence and stability of the eight steady states of the model. We study the global stability of all steady states based on the construction of suitable Lyapunov functions and usage of Lyapunov-LaSalle asymptotic stability theorem. Lastly, numerical simulations are carried out in order to verify the validity of our theoretical results.</p></abstract>

scholarly journals Complex Dynamics of an Impulsive Chemostat Model

2019 ◽  
Vol 29 (08) ◽  
pp. 1950101 ◽  
Author(s):  
Jin Yang ◽  
Yuanshun Tan ◽  
Robert A. Cheke
Keyword(s):  
Periodic Solution ◽  
Global Stability ◽  
Substrate Concentration ◽  
Complex Dynamics ◽  
Control Strategies ◽  
Phase Portraits ◽  
Global Dynamics ◽  
Chemostat Model ◽  
Existence And Stability ◽  
Theoretical Results

We propose a novel impulsive chemostat model with the substrate concentration as the basis for the implementation of control strategies, and then investigate the model’s global dynamics. The exact domains of the impulsive and phase sets are discussed in the light of phase portraits of the model, and then we define the Poincaré map and study its complex properties. Furthermore, the existence and stability of the microorganism eradication periodic solution are addressed, and the analysis of a transcritical bifurcation reveals that an order-1 periodic solution is generated. We also provide the conditions for the global stability of an order-1 periodic solution and show the existence of order-[Formula: see text] [Formula: see text] periodic solutions. Moreover, the PRCC results and bifurcation analyses not only substantiate our results, but also indicate that the proposed system exists with complex dynamics. Finally, biological implications related to the theoretical results are discussed.

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 A Discrete Model for HIV Infection with Distributed Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Brahim EL Boukari ◽  
Khalid Hattaf ◽  
Noura Yousfi
Keyword(s):  
Hiv Infection ◽  
Global Stability ◽  
Time Delays ◽  
Discrete Model ◽  
Distributed Delay ◽  
Continuous Model ◽  
Distributed Time Delays ◽  
A Cell ◽  
The Times ◽  
Theoretical Results

We give a consistent discretization of a continuous model of HIV infection, with distributed time delays to express the lag between the times when the virus enters a cell and when the cell becomes infected. The global stability of the steady states of the model is determined and numerical simulations are presented to illustrate our theoretical results.

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