Global properties and bifurcation analysis of an HIV-1 infection model with two target cells

2017 ◽  
Vol 37 (3) ◽  
pp. 3455-3472 ◽  
Author(s):  
Yongqi Liu ◽  
Xuanliang Liu
Keyword(s):  
Bifurcation Analysis ◽  
Infection Model ◽  
Target Cells ◽  
Global Properties ◽  
Hiv 1

Global properties of a cell mediated immunity in HIV infection model with two classes of target cells and distributed delays

2014 ◽  
Vol 07 (05) ◽  
pp. 1450055 ◽  
Author(s):  
A. M. Elaiw ◽  
R. M. Abukwaik ◽  
E. O. Alzahrani
Keyword(s):  
Immune Response ◽  
Steady State ◽  
Hiv Infection ◽  
Infection Model ◽  
Target Cells ◽  
Cell Mediated Immunity ◽  
Globally Asymptotically Stable ◽  
Global Properties ◽  
Hiv Infection Model ◽  
Ctl Immune Response

In this paper, we study the global properties of a human immunodeficiency virus (HIV) infection model with cytotoxic T lymphocytes (CTL) immune response. The model is a six-dimensional that describes the interaction of the HIV with two classes of target cells, CD4+ T cells and macrophages. The infection rate is given by saturation functional response. Two types of distributed time delays are incorporated into the model to describe the time needed for infection of target cell and virus replication. Using the method of Lyapunov functional, we have established that the global stability of the model is determined by two threshold numbers, the basic infection reproduction number R0 and the immune response activation number [Formula: see text]. We have proven that if R0 ≤ 1, then the uninfected steady state is globally asymptotically stable (GAS), if [Formula: see text], then the infected steady state without CTL immune response is GAS, and if [Formula: see text], then the infected steady state with CTL immune response is GAS.

ANALYSIS OF AN AGE-STRUCTURED HIV-1 INFECTION MODEL WITH LOGISTIC TARGET CELL GROWTH

2020 ◽  
Vol 28 (04) ◽  
pp. 927-944
Author(s):  
HUIJUAN LIU ◽  
FEI XU ◽  
JIA-FANG ZHANG
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Logistic Growth ◽  
Infection Model ◽  
Target Cells ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Age Structured ◽  
Hiv 1 ◽  
The Basic Reproduction Number

In this work, we construct an age-structured HIV-1 infection model to investigate the interplay between [Formula: see text] cells and viruses. In our model, we assume that the variations in the death rate of productively infected [Formula: see text] cells and the production rate of virus in infected cells are all age-dependent, and the target cells follow logistic growth. We perform mathematical analysis and prove the persistence of the semi-flow of the system. We calculate the basic reproduction number and prove the local and global stability of the steady states. We show that if the basic reproduction number is less than one, the disease-free equilibrium is globally asymptotically stable, and if the basic reproduction number is greater than one, the infected steady state is locally asymptotically stable.

A DELAYED HIV-1 MODEL WITH MULTIPLE TARGET CELLS AND GENERAL NONLINEAR INCIDENCE RATE

2013 ◽  
Vol 21 (04) ◽  
pp. 1340012 ◽  
Author(s):  
BING LI ◽  
SHENGQIANG LIU
Keyword(s):  
T Cells ◽  
Infection Model ◽  
Target Cells ◽  
Time Lags ◽  
Multiple Target ◽  
Nonlinear Incidence ◽  
Virus Particles ◽  
Reproduction Numbers ◽  
Incidence Functions ◽  
Hiv 1

We investigate a delayed HIV-1 infection model with general nonlinear incidence functions and two classes of target cells: CD4+ T-cells and macrophages. To account for the time lags between viruses' entry into the corresponding two types of target cells and the production of new virus particles, we incorporate four distributed intracellular delays into the model. We show that the basic reproduction number ℜ0 is the sum of the basic reproduction numbers of HIV-1 infection with CD4+ T-cells and that with macrophages; moreover, if ℜ0 is less than or equal to one, then the HIV-1 infection is cleared from the T-cell population and macrophages; whereas if ℜ0 is larger than one, then the viral concentration maintains at some constant level. It is shown, from both our analytic and numeric results, that ignoring the contributions of macrophages to HIV-1 infection and production will underestimate both the risk of HIV-1 infection and the viral load when persisting. This highlights the important effects of multiple target cells on HIV-1 infection.

Stability analysis of delay integro-differential equations of HIV-1 infection model

2020 ◽  
Vol 27 (3) ◽  
pp. 331-340
Author(s):  
Nigar Ali ◽  
Gul Zaman ◽  
Il Hyo Jung
Keyword(s):  
Differential Equations ◽  
Latent Period ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Infection Model ◽  
Target Cells ◽  
Globally Asymptotically Stable ◽  
Delay Term ◽  
Delay Differential ◽  
Hiv 1

AbstractIn this paper, the analysis of an HIV-1 epidemic model is presented by incorporating a distributed intracellular delay. The delay term represents the latent period between the time that the target cells are contacted by the virus and the time the virions penetrated into the cells. To understand the analysis of our proposed model, the Rouths–Hurwiz criterion and general theory of delay differential equations are used. It is shown that the infection free equilibrium and the chronic-infection equilibrium are locally as well as globally asymptotically stable, under some conditions on the basic reproductive number {R_{0}}. Furthermore, the obtained results show that the value of {R_{0}} can be decreased by increasing the delay. Therefore, any drugs that can prolong the latent period will help to control the HIV-1 infection.

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