Quasilinearization-Lagrangian method to solve the HIV infection model of CD4 $$^+$$ + T cells

In this work, we use Padé’s approaches in solving a system of ordinary nonlinear differential equationswhich arises in the model for HIV infection of CD4+T cells. Some graphs are presented to show the reliabilityand simplicity of this method as well as the algorithms implemented in the analysis of the model.

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An exponential Galerkin method for solutions of HIV infection model of CD4+ T-cells

Computational Biology and Chemistry ◽

10.1016/j.compbiolchem.2016.12.006 ◽

2017 ◽

Vol 67 ◽

pp. 205-212 ◽

Cited By ~ 10

Author(s):

Şuayip Yüzbaşı ◽

Murat Karaçayır

Keyword(s):

T Cells ◽

Hiv Infection ◽

Galerkin Method ◽

Cd4 T Cells ◽

Infection Model ◽

Hiv Infection Model

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Bifurcation Analysis of an Age Structured HIV Infection Model with Both Virus-to-Cell and Cell-to-Cell Transmissions

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127418501092 ◽

2018 ◽

Vol 28 (09) ◽

pp. 1850109 ◽

Cited By ~ 6

Author(s):

Xiangming Zhang ◽

Zhihua Liu

Keyword(s):

T Cells ◽

Hopf Bifurcation ◽

Hiv Infection ◽

Bifurcation Analysis ◽

Dynamical Behavior ◽

Infection Model ◽

Positive Equilibrium ◽

Semilinear Equations ◽

Age Structured ◽

Hiv Infection Model

We make a mathematical analysis of an age structured HIV infection model with both virus-to-cell and cell-to-cell transmissions to understand the dynamical behavior of HIV infection in vivo. In the model, we consider the proliferation of uninfected CD[Formula: see text] T cells by a logistic function and the infected CD[Formula: see text] T cells are assumed to have an infection-age structure. Our main results concern the Hopf bifurcation of the model by using the theory of integrated semigroup and the Hopf bifurcation theory for semilinear equations with nondense domain. Bifurcation analysis indicates that there exist some parameter values such that this HIV infection model has a nontrivial periodic solution which bifurcates from the positive equilibrium. The numerical simulations are also carried out.

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Parameters estimation of HIV infection model of CD4+T-cells by applying orthonormal Bernstein collocation method

International Journal of Biomathematics ◽

10.1142/s1793524518500201 ◽

2018 ◽

Vol 11 (02) ◽

pp. 1850020 ◽

Cited By ~ 5

Author(s):

Farshid Mirzaee ◽

Nasrin Samadyar

Keyword(s):

T Cells ◽

Nonlinear System ◽

Hiv Infection ◽

Initial Conditions ◽

Bernstein Polynomials ◽

Nonlinear Ordinary Differential Equation ◽

Parameters Estimation ◽

Infection Model ◽

Algebraic Equations ◽

Hiv Infection Model

The HIV infection model of CD4[Formula: see text][Formula: see text]T-cells corresponds to a class of nonlinear ordinary differential equation systems. In this study, we provide the approximate solution of this model by using orthonormal Bernstein polynomials (OBPs). By applying the proposed method, the nonlinear system of ordinary differential equations reduces to a nonlinear system of algebraic equations which can be solved by using a suitable numerical method such as Newton’s method. We prove some useful theorems concerning the convergence and error estimate associated to the present method. Finally, we apply the proposed method to get the numerical solution of this model with the arbitrary initial conditions and values. Furthermore, the numerical results obtained by the suggested method are compared with the results achieved by other previous methods. These results indicate that this method agrees with other previous methods.

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Global Dynamics of an HIV Infection Model with Two Classes of Target Cells and Distributed Delays

Discrete Dynamics in Nature and Society ◽

10.1155/2012/253703 ◽

2012 ◽

Vol 2012 ◽

pp. 1-13 ◽

Cited By ~ 12

Author(s):

A. M. Elaiw

Keyword(s):

T Cells ◽

Steady State ◽

Hiv Infection ◽

Infection Model ◽

Target Cells ◽

Global Dynamics ◽

Asymptotically Stable ◽

Globally Asymptotically Stable ◽

Hiv Infection Model ◽

Nonlinear Delay

We investigate the global dynamics of an HIV infection model with two classes of target cells and multiple distributed intracellular delays. The model is a 5-dimensional nonlinear delay ODEs that describes the interaction of the HIV with two classes of target cells, CD4+T cells and macrophages. The incidence rate of infection is given by saturation functional response. The model has two types of distributed time delays describing time needed for infection of target cell and virus replication. This model can be seen as a generalization of several models given in the literature describing the interaction of the HIV with one class of target cells, CD4+T cells. Lyapunov functionals are constructed to establish the global asymptotic stability of the uninfected and infected steady states of the model. We have proven that if the basic reproduction numberR0is less than unity then the uninfected steady state is globally asymptotically stable, and ifR0>1then the infected steady state exists and it is globally asymptotically stable.

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Singly Diagonally Implicit Block Backward Differentiation Formulas for HIV Infection of CD4+T Cells

Symmetry ◽

10.3390/sym11050625 ◽

2019 ◽

Vol 11 (5) ◽

pp. 625

Author(s):

Saufianim Jana Aksah ◽

Zarina Bibi Ibrahim

Keyword(s):

T Cells ◽

Hiv Infection ◽

Approximate Solutions ◽

Infection Model ◽

Triangular Form ◽

Differentiation Formula ◽

Fully Implicit ◽

Backward Differentiation Formulas ◽

Hiv Infection Model ◽

Differentiation Formulas

In this study, a singly diagonally implicit block backward differentiation formula (SDIBBDF) was proposed to approximate solutions for a dynamical HIV infection model of CD 4 + T cells. A SDIBBDF method was developed to overcome difficulty when implementing the fully implicit method by deriving the proposed method in lower triangular form with equal diagonal coefficients. A comparative analysis between the proposed method, BBDF, classical Euler, fourth-order Runge-Kutta (RK4) method, and a Matlab solver was conducted. The numerical results proved that the SDIBBDF method was more efficient in solving the model than the methods to be compared.

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A numerical method for the solutions of the HIV infection model of CD4+T-cells

International Journal of Biomathematics ◽

10.1142/s179352451750098x ◽

2017 ◽

Vol 10 (07) ◽

pp. 1750098 ◽

Cited By ~ 4

Author(s):

Şuayip Yüzbaşı ◽

Nurbol Ismailov

Keyword(s):

T Cells ◽

Hiv Infection ◽

Operational Matrix ◽

Approximate Solutions ◽

Infection Model ◽

Algebraic Equations ◽

Immunodeficiency Virus ◽

Taylor Polynomials ◽

Hiv Infection Model ◽

Operational Matrix Of Integration

In this paper, the human immunodeficiency virus (HIV) infection model of CD[Formula: see text][Formula: see text]T-cells is considered. In order to numerically solve the model problem, an operational method is proposed. For that purpose, we construct the operational matrix of integration for bases of Taylor polynomials. Then, by using this matrix operation and approximation by polynomials, the HIV infection problem is transformed into a system of algebraic equations, whose roots are used to determine the approximate solutions. An important feature of the method is that it does not require collocation points. In addition, an error estimation technique is presented. We apply the present method to two numerical examples and compare our results with other methods.

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