scholarly journals Analysis of General Humoral Immunity HIV Dynamics Model with HAART and Distributed Delays

Mathematics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 157 ◽  
Author(s):  
A. Elaiw ◽  
E. Elnahary
Keyword(s):  
Hiv Infection ◽  
The Body ◽  
Target Cells ◽  
Nonlinear Functions ◽  
Dynamics Model ◽  
Therapeutic Modalities ◽  
Hiv Dynamics ◽  
Highly Active ◽  
Infected Cells ◽  
Theoretical Results

This paper deals with the study of an HIV dynamics model with two target cells, macrophages and CD4 + T cells and three categories of infected cells, short-lived, long-lived and latent in order to get better insights into HIV infection within the body. The model incorporates therapeutic modalities such as reverse transcriptase inhibitors (RTIs) and protease inhibitors (PIs). The model is incorporated with distributed time delays to characterize the time between an HIV contact of an uninfected target cell and the creation of mature HIV. The effect of antibody on HIV infection is analyzed. The production and removal rates of the ten compartments of the model are given by general nonlinear functions which satisfy reasonable conditions. Nonnegativity and ultimately boundedness of the solutions are proven. Using the Lyapunov method, the global stability of the equilibria of the model is proven. Numerical simulations of the system are provided to confirm the theoretical results. We have shown that the antibodies can play a significant role in controlling the HIV infection, but it cannot clear the HIV particles from the plasma. Moreover, we have demonstrated that the intracellular time delay plays a similar role as the Highly Active Antiretroviral Therapies (HAAT) drugs in eliminating the HIV particles.

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.

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.

GLOBAL ANALYSIS OF AN EXTENDED HIV DYNAMICS MODEL WITH GENERAL INCIDENCE RATE

2015 ◽  
Vol 23 (03) ◽  
pp. 401-421
Author(s):  
AHMED ELAIW ◽  
NADA. ALMUALLEM ◽  
XIA WANG
Keyword(s):  
Global Stability ◽  
Incidence Rate ◽  
Global Analysis ◽  
Drug Efficacy ◽  
Target Cells ◽  
Qualitative Behavior ◽  
Global Dynamics ◽  
Dynamics Model ◽  
Hiv Dynamics ◽  
Infected Cells

The objective of this work is to investigate the qualitative behavior of an Human Immunodeficiency Virus (HIV) dynamics model with two types of cocirculating target cells and under the effect of anti-viral drug therapy. The model takes into account both short-lived infected cells and long-lived chronically infected cells. In the two types of target cells, the drug efficacy is assumed to be different. The incidence rate of virus infection is given by general functional response. We have derived the basic reproduction number which determines the global dynamics of the model. We have established a set of conditions which are sufficient to investigate the global stability of the equilibria of the model. The global stability analysis of the model has been established using the Lyapunov method. Numerical simulations have been performed for the model with a specific form of the incidence rate function. We have shown that the numerical and theoretical results are consistent.

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.

scholarly journals Pharmacokinetics of antiretroviral drugs in infancy

2009 ◽  
Vol 10 (4) ◽  
pp. 54
Author(s):  
Helen McIlleron ◽  
Hermien Gous
Keyword(s):  
Hiv Infection ◽  
Antiretroviral Treatment ◽  
Hiv Transmission ◽  
Antiretroviral Drugs ◽  
The Body ◽  
World Health ◽  
Highly Active ◽  
Drug Concentrations ◽  
One Year ◽  
Health Organization

Infancy (from birth until 1 year of age) is a time of rapid changes within the body of a child. These changes affect pharmacokinetics in many ways. The CHER study1 showed that early antiretroviral treatment reduces mortality and disease progression amongst infants acquiring HIV infection before 12 weeks of age. As a result the World Health Organization has recently revised treatment initiation recommendations in children less than one year of age: all infants under 12 months of age with confirmed HIV infection should be started on antiretroviral therapy, irrespective of clinical or immunological stage2. Dosing in infants is challenging because drug concentrations are highly variable, there is frequently scant pharmacokinetic information in young children, and few suitable drug formulations are available. Furthermore, adherence to treatment is reliant on the caregiver, rather than the patient. Peri- and postnatal HIV transmission are reduced by maternal highly active antiretroviral treatment (HAART). However, the benefits and risks to breast fed infants of exposure to maternal antiretroviral drugs during lactation are poorly understood. In this article we review the pharmacokinetics of antiretroviral drugs relevant to South African infants, and highlight some of the challenges to delivering antiretroviral treatment in safe and effective doses.

scholarly journals The Phagocytic Code Regulating Phagocytosis of Mammalian Cells

2021 ◽  
Vol 12 ◽  
Author(s):  
Tom O. J. Cockram ◽  
Jacob M. Dundee ◽  
Alma S. Popescu ◽  
Guy C. Brown
Keyword(s):  
Mammalian Cells ◽  
The Body ◽  
Psychiatric Disease ◽  
Target Cells ◽  
Immune Disease ◽  
Neuronal Synapses ◽  
Galectin 3 ◽  
A Cell ◽  
Infected Cells ◽  
Dying Cells

Mammalian phagocytes can phagocytose (i.e. eat) other mammalian cells in the body if they display certain signals, and this phagocytosis plays fundamental roles in development, cell turnover, tissue homeostasis and disease prevention. To phagocytose the correct cells, phagocytes must discriminate which cells to eat using a ‘phagocytic code’ - a set of over 50 known phagocytic signals determining whether a cell is eaten or not - comprising find-me signals, eat-me signals, don’t-eat-me signals and opsonins. Most opsonins require binding to eat-me signals – for example, the opsonins galectin-3, calreticulin and C1q bind asialoglycan eat-me signals on target cells - to induce phagocytosis. Some proteins act as ‘self-opsonins’, while others are ‘negative opsonins’ or ‘phagocyte suppressants’, inhibiting phagocytosis. We review known phagocytic signals here, both established and novel, and how they integrate to regulate phagocytosis of several mammalian targets - including excess cells in development, senescent and aged cells, infected cells, cancer cells, dead or dying cells, cell debris and neuronal synapses. Understanding the phagocytic code, and how it goes wrong, may enable novel therapies for multiple pathologies with too much or too little phagocytosis, such as: infectious disease, cancer, neurodegeneration, psychiatric disease, cardiovascular disease, ageing and auto-immune disease.

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.

scholarly journals Post-treatment control of HIV infection

2015 ◽  
Vol 112 (17) ◽  
pp. 5467-5472 ◽  
Author(s):  
Jessica M. Conway ◽  
Alan S. Perelson
Keyword(s):  
Hiv Infection ◽  
Primary Infection ◽  
Population Level ◽  
Post Treatment ◽  
Latent Reservoir ◽  
Target Cells ◽  
Elite Controllers ◽  
Treatment Control ◽  
Treatment Termination ◽  
Infected Cells

Antiretroviral therapy (ART) for HIV is not a cure. However, recent studies suggest that ART, initiated early during primary infection, may induce post-treatment control (PTC) of HIV infection with HIV RNA maintained at <50 copies per mL. We investigate the hypothesis that ART initiated early during primary infection permits PTC by limiting the size of the latent reservoir, which, if small enough at treatment termination, may allow the adaptive immune response to prevent viral rebound (VR) and control infection. We use a mathematical model of within host HIV dynamics to capture interactions among target cells, productively infected cells, latently infected cells, virus, and cytotoxic T lymphocytes (CTLs). Analysis of our model reveals a range in CTL response strengths where a patient may show either VR or PTC, depending on the size of the latent reservoir at treatment termination. Below this range, patients will always rebound, whereas above this range, patients are predicted to behave like elite controllers. Using data on latent reservoir sizes in patients treated during primary infection, we also predict population-level VR times for noncontrollers consistent with observations.

Sign in / Sign up

Export Citation Format

Share Document