The Laplace Adomian Decomposition Method for solving a model for HIV infection of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si13.gif" display="inline" overflow="scroll"><mml:mi>C</mml:mi><mml:mi>D</mml:mi><mml:msup><mml:mrow><mml:mn>4</mml:mn></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup><mml:mi>T</mml:mi></mml:math>cells

Ongun, Mevlüde Yakit

doi:10.1016/j.mcm.2010.09.009

Cited by 112 publications

(24 citation statements)

References 15 publications

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“…Tere are some numerical methods to solve model (97). Merdan [24] solved the model by homotopy perturbation method, Ongun [25] applied the Laplace Adomian decomposition method to solve the model, Merdan et al [26] applied the Padè approximate method and the modifed variational iteration method (VIM) for solving (97), Yüzbas ¸i [27] used the Bessel collocation method. A modifcation of the classical Laplace Adomian decomposition method is used by Doǧan [28] and fnally, Srivastava et al [29] applied the diferential transform method (DTM) to solve the model.…”

Section: Numerical Resultsmentioning

confidence: 99%

An Analytical Study on Two High-Order Hybrid Methods to Solve Systems of Nonlinear Equations

Darvishi

2023

Journal of Mathematics

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In order to solve systems of nonlinear equations, two novel iterative methods are presented. The successive over-relaxation method and the Chebyshev-like iterative methods to solve systems of nonlinear equations have combined to obtain the new algorithms. By this combination, two powerful hybrid methods are obtained. Necessary conditions for convergence of these methods are presented. Furthermore, the stability analysis of both algorithms is investigated. These algorithms are applied for solving two real stiff systems of ordinary differential equations. These systems arise from an HIV spreading model and an SIR model of an epidemic which formulates the spread of a nonfatal disease in a certain population. Numerical results show promising convergence and stability for both new hybrid methods.

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Section: Numerical Resultsmentioning

confidence: 99%

An Analytical Study on Two High-Order Hybrid Methods to Solve Systems of Nonlinear Equations

Darvishi

2023

Journal of Mathematics

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“…The study by Bushnaq et al [10] investigated the stability existence of steady states of HIV/AIDS mode with fractional derivatives and explored the role of memory in the dynamics of HIV infection. The authors in [11][12][13][14] implemented different techniques and methods to show the path-tracking behavior of the dynamics of HIV. The main objective of the current study is to formulate the dynamics of HIV with a variable source term instead of a constant term for the supply of new CD4 + T-cells from the thymus.…”

Section: Introductionmentioning

confidence: 99%

Fractional Dynamics of HIV with Source Term for the Supply of New CD4+ T-Cells Depending on the Viral Load via Caputo–Fabrizio Derivative

et al. 2021

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Human immunodeficiency virus (HIV) is a life life-threatening and serious infection caused by a virus that attacks CD4+ T-cells, which fight against infections and make a person susceptible to other diseases. It is a global public health problem with no cure; therefore, it is highly important to study and understand the intricate phenomena of HIV. In this article, we focus on the numerical study of the path-tracking damped oscillatory behavior of a model for the HIV infection of CD4+ T-cells. We formulate fractional dynamics of HIV with a source term for the supply of new CD4+ T-cells depending on the viral load via the Caputo–Fabrizio derivative. In the formulation of fractional HIV dynamics, we replaced the constant source term for the supply of new CD4+ T-cells from the thymus with a variable source term depending on the concentration of the viral load, and introduced a term that describes the incidence of the HIV infection of CD4+ T-cells. We present a novel numerical scheme for fractional view analysis of the proposed model to highlight the solution pathway of HIV. We inspect the periodic and chaotic behavior of HIV for the given values of input factors using numerical simulations.

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“…A mathematical model can be formulated to gain nonintuitive insights of the HIV transmission dynamics. Many mathematical models for HIV/AIDS transmission dynamics have been formulated and their corresponding numerical solutions have been presented [10]- [13]. They applied the nonstandard finite difference scheme and the differential transformation method for solving HIV mathematical models.…”

Section: Introductionmentioning

confidence: 99%

Application of Differential Transformation Method for Solving HIV Model with Anti-Viral Treatment

Bunga

Ndii

2020

BAREKENG

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Mathematical models have been widely used to understand complex phenomena. Generally, the model is in the form of system of differential equations. However, when the model becomes complex, analytical solutions are not easily found and hence a numerical approach has been used. A number of numerical schemes such as Euler, Runge-Kutta, and Finite Difference Scheme are generally used. There are also alternative numerical methods that can be used to solve system of differential equations such as the nonstandard finite difference scheme (NSFDS), the Adomian decomposition method (ADM), Variation iteration method (VIM), and the differential transformation method (DTM). In this paper, we apply the differential transformation method (DTM) to solve system of differential equations. The DTM is semi-analytical numerical technique to solve the system of differential equations and provides an iterative procedure to obtain the power series of the solution in terms of initial value parameters.. In this paper, we present a mathematical model of HIV with antiviral treatment and construct a numerical scheme based on the differential transformation method (DTM) for solving the model. The results are compared to that of Runge-Kutta method. We find a good agreement of the DTM and the Runge-Kutta method for smaller time step but it fails in the large time step.

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The Laplace Adomian Decomposition Method for solving a model for HIV infection ofCD4+Tcells

Cited by 112 publications

References 15 publications

An Analytical Study on Two High-Order Hybrid Methods to Solve Systems of Nonlinear Equations

An Analytical Study on Two High-Order Hybrid Methods to Solve Systems of Nonlinear Equations

Fractional Dynamics of HIV with Source Term for the Supply of New CD4+ T-Cells Depending on the Viral Load via Caputo–Fabrizio Derivative

Application of Differential Transformation Method for Solving HIV Model with Anti-Viral Treatment

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