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

Yüzbaşı, Şuayip; Ismailov, Nurbol

doi:10.1142/s179352451750098x

Cited by 12 publications

(3 citation statements)

References 16 publications

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“…For the numerical investigation, Ahmed et al [ 36 ] proposed an extended temporal model of HIV with medication treatment impact using the backward Euler and Crank-Nicolson techniques. The HIV model of T-cells was explored by Yüzbaşı [ 37 ], and an operational technique was suggested to numerically address the model problem. Merdan [ 38 ] utilised the homotopy perturbation method (HPM) to examine the numerical outcomes of HIV model.…”

Section: Introductionmentioning

confidence: 99%

A Higher-Order Galerkin Time Discretization and Numerical Comparisons for Two Models of HIV Infection

Attaullah

Yüzbaşı

Alyobi

et al. 2022

Computational and Mathematical Methods in Medicine

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Human immunodeficiency virus (HIV) infection affects the immune system, particularly white blood cells known as CD4+ T-cells. HIV destroys CD4+ T-cells and significantly reduces a human’s resistance to viral infectious diseases as well as severe bacterial infections, which can lead to certain illnesses. The HIV framework is defined as a system of nonlinear first-order ordinary differential equations, and the innovative Galerkin technique is used to approximate the solutions of the model. To validate the findings, solve the model employing the Runge-Kutta (RK) technique of order four. The findings of the suggested techniques are compared with the results obtained from conventional schemes such as MuHPM, MVIM, and HPM that exist in the literature. Furthermore, the simulations are performed with different time step sizes, and the accuracy is measured at various time intervals. The numerical computations clearly demonstrate that the Galerkin scheme, in contrast to the Runge-Kutta scheme, provides incredibly precise solutions at relatively large time step sizes. A comparison of the solutions reveals that the obtained results through the Galerkin scheme are in fairly good agreement with the RK4 scheme in a given time interval as compared to other conventional schemes. Moreover, having performed various numerical tests for assessing the efficiency and computational cost (in terms of time) of the suggested schemes, it is observed that the Galerkin scheme is noticeably slower than the Runge-Kutta scheme. On the other hand, this work is also concerned with the path tracking and damped oscillatory behaviour of the model with a variable supply rate for the generation of new CD4+ T-cells (based on viral load concentration) and the HIV infection incidence rate. Additionally, we investigate the influence of various physical characteristics by varying their values and analysing them using graphs. The investigations indicate that the lateral system ensured more accurate predictions than the previous model.

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Section: Introductionmentioning

confidence: 99%

A Higher-Order Galerkin Time Discretization and Numerical Comparisons for Two Models of HIV Infection

Attaullah

Yüzbaşı

Alyobi

et al. 2022

Computational and Mathematical Methods in Medicine

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“…In sciences and engineering, the analysis of linear and non-linear differential equations is of great importance. Differential equations have appeared in the study of many topics as a robust and quite well-organized mathematical tool, such as circuit problems (Filobello-Nino et al, 2012;Vazquez-Leal et al, 2014Miranda-Villatoro et al, 2018;Popovi c, 2018;Mukhiya et al, 2020), infectious model (Doungmo Goufo et al, 2020;Calatayud et al, 2020aCalatayud et al, , 2020bYüzbas i and _ Ismailov, 2017;Faraz et al, 2020;Khan et al, 2012), soliton wave theory (Khan, 2018(Khan, , 2020a(Khan, , 2020bSaha Ray, 2018), fluid mechanics (Khan, 2013(Khan, , 2014(Khan, , 2011 and many more complex problems (Turkyilmazoglu, 2011;Calatayud et al, 2020aCalatayud et al, , 2020bSlota et al, 2019;He et al, 2019;He, 2019). Suggesting an effective approximate analytical solution to a non-linear differential equation is a challenging task.…”

Section: Introductionmentioning

confidence: 99%

“…The emerging strongly non-linear differential equations in circuit design (Tohyama et al, 2010;Kassem and Abdelaziz, 2015) were performed only numerically. Recently, researchers demonstrated significant attention in suggesting various techniques for solving analytical solutions for circuit-related differential equations (Wang and Chiang, 2014;Vazquez-Leal et al, 2013).…”

Section: Introductionmentioning

confidence: 99%

Simple use of the Maclaurin series method for linear and non-linear differential equations arising in circuit analysis

Khan

Faraz

2021

COMPEL

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Purpose The purpose of this paper is to investigate the circuit analysis differential equations, which play an important role in the field of electrical and electronic engineering, and it was necessary to propose a very simple and direct method to obtain approximate solutions for the linear or non-linear differential equations, which should be simple for engineers to understand. Design/methodology/approach This paper introduces a simple novel Maclaurin series method (MSM) to propose an approximate novel solution in the area of circuit analysis for linear and non-linear differential equations. These equations describe the alternating current circuit of the resistor–capacitor, which evaluates the effect of non-linear current resistance. Linear and non-linear differential equations are evaluated as a computational analysis to assist the research, which reveals that the MSM is incredibly simple and effective. Findings Simulation findings indicate that the achieved proposed solution using the novel suggested approach is identical to the exact solutions mentioned in the literature. As the Maclaurin series is available to all non-mathematicians, this paper reflects mostly on theoretical implementations of the numerous circuit problems that occur in the field of electrical engineering. Originality/value A very simple and efficient method has been proposed in this paper, which is very easy to understand for even non-mathematicians such as engineers. The paper introduced a method of the Maclaurin series to solve non-linear differential equations resulting from the study of the circuits. The MSM mentioned here will be a useful tool in areas of physical and engineering anywhere the problem of the circuits is studied.

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An Optimization Method Based on the Generalized Polynomials for a Model of HIV Infection of $$\hbox {CD4}^{+}$$ T Cells

Hassani

Mehrabi

Naraghirad

et al. 2020

Iran J Sci Technol Trans Sci

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

Cited by 12 publications

References 16 publications

A Higher-Order Galerkin Time Discretization and Numerical Comparisons for Two Models of HIV Infection

A Higher-Order Galerkin Time Discretization and Numerical Comparisons for Two Models of HIV Infection

Simple use of the Maclaurin series method for linear and non-linear differential equations arising in circuit analysis

An Optimization Method Based on the Generalized Polynomials for a Model of HIV Infection of $$\hbox {CD4}^{+}$$ T Cells

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