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

2017 ◽  
Vol 10 (07) ◽  
pp. 1750098 ◽  
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.

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

2018 ◽  
Vol 11 (02) ◽  
pp. 1850020 ◽  
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.

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

Symmetry ◽  
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.

An exponential collocation method for the solutions of the HIV infection model of CD4+T cells

2016 ◽  
Vol 09 (03) ◽  
pp. 1650036 ◽  
Author(s):  
Şuayip Yüzbaşı
Keyword(s):  
Hiv Infection ◽  
Model Problem ◽  
Approximate Solutions ◽  
Infection Model ◽  
Algebraic Equations ◽  
Exponential Polynomials ◽  
Collocation Points ◽  
Nonlinear Algebraic Equations ◽  
Exponential Method ◽  
Hiv Infection Model

In this paper, an exponential method is presented for the approximate solutions of the HIV infection model of CD4[Formula: see text]T. The method is based on exponential polynomials and collocation points. This model problem corresponds to a system of nonlinear ordinary differential equations. Matrix relations are constructed for the exponential functions. By aid of these matrix relations and the collocation points, the proposed technique transforms the model problem into a system of nonlinear algebraic equations. By solving the system of the algebraic equations, the unknown coefficients are computed and thus the approximate solutions are obtained. The applications of the method for the considered problem are given and the comparisons are made with the other methods.

scholarly journals Threshold dynamics and threshold analysis of HIV infection model with treatment

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Zhimin Chen ◽  
Xiuxiang Liu ◽  
Liling Zeng
Keyword(s):  
Hiv Infection ◽  
Time Delays ◽  
Dynamical Behavior ◽  
Infection Model ◽  
Threshold Dynamics ◽  
Positive Equilibrium ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Immunodeficiency Virus ◽  
Hiv Infection Model

Abstract In this paper, a human immunodeficiency virus (HIV) infection model that includes a protease inhibitor (PI), two intracellular delays, and a general incidence function is derived from biologically natural assumptions. The global dynamical behavior of the model in terms of the basic reproduction number $\mathcal{R}_{0}$ R 0 is investigated by the methods of Lyapunov functional and limiting system. The infection-free equilibrium is globally asymptotically stable if $\mathcal{R}_{0}\leq 1$ R 0 ≤ 1 . If $\mathcal{R}_{0}>1$ R 0 > 1 , then the positive equilibrium is globally asymptotically stable. Finally, numerical simulations are performed to illustrate the main results and to analyze thre effects of time delays and the efficacy of the PI on $\mathcal{R}_{0}$ R 0 .

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

2018 ◽  
Vol 28 (09) ◽  
pp. 1850109 ◽  
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.

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

SeMA Journal ◽  
2017 ◽  
Vol 75 (2) ◽  
pp. 271-283 ◽  
Author(s):  
Kourosh Parand ◽  
Zahra Kalantari ◽  
Mehdi Delkhosh
Keyword(s):  
T Cells ◽  
Hiv Infection ◽  
Cd4 T Cells ◽  
Lagrangian Method ◽  
Infection Model ◽  
Hiv Infection Model

Stochastic numerical technique for solving HIV infection model of CD4+ T cells

2020 ◽  
Vol 135 (5) ◽  
Author(s):  
Muhammad Umar ◽  
Zulqurnain Sabir ◽  
Fazli Amin ◽  
Juan L. G. Guirao ◽  
Muhammad Asif Zahoor Raja
Keyword(s):  
T Cells ◽  
Hiv Infection ◽  
Cd4 T Cells ◽  
Numerical Technique ◽  
Infection Model ◽  
Hiv Infection Model

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

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
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.

Shifted Boubaker Lagrangian approach for solving biological systems

2018 ◽  
Vol 11 (03) ◽  
pp. 1850039 ◽  
Author(s):  
Kourosh Parand ◽  
Hossein Yousefi ◽  
Mina Fotouhifar ◽  
Mehdi Delkhosh ◽  
Mehdi Hosseinzadeh
Keyword(s):  
Mathematical Models ◽  
Hantavirus Infection ◽  
Infection Model ◽  
Algebraic Equations ◽  
Sir Epidemic Model ◽  
Sir Epidemic ◽  
Immunodeficiency Virus ◽  
Nonlinear Algebraic Equations ◽  
Newton Iteration Method ◽  
Hiv Infection Model

Mathematical models and computer simulations are useful experimental tools for building and testing theories. Many mathematical models in biology can be formulated by a nonlinear system of ordinary differential equations. This work deals with the numerical solution of the hantavirus infection model, the human immunodeficiency virus (HIV) infection model of CD4[Formula: see text]T cells and the susceptible–infected–removed (SIR) epidemic model using a new reliable algorithm based on shifted Boubaker Lagrangian (SBL) method. This method reduces the solution of such system to a system of linear or nonlinear algebraic equations which are solved using the Newton iteration method. The obtained results of the proposed method show highly accurate and valid for an arbitrary finite interval. Also, those are compared with fourth-order Runge–Kutta (RK4) method and with the solutions obtained by some other methods in the literature.

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