Spectral solutions of fractional differential equations modelling combined drug therapy for HIV infection

Thirumalai, Sagithya; Yüzbaşı, Şuayip

doi:10.1016/j.chaos.2021.111234

Cited by 9 publications

(3 citation statements)

References 20 publications

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“…Recently, the subject of fractional calculus has been extensively developed and studied by many academics due to its applications in numerous branches of applied sciences, technology, and engineering. Examples include engineering [1], ecology [2], biology [3], medicine [4], chemistry [5], animal science [6], finance [7], control theory [8], and other branches. In recent decades, Hilfer defined a generalized fractional derivative of Riemann-Liouville (R-L), which includes fractional derivatives of Caputo and R-L [9].…”

Section: Introductionmentioning

confidence: 99%

Maximum Principle for Nonlinear Fractional Differential Equations with the Hilfer Derivative

Elbukhari

Fan

2023

Fractal Fract

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In this paper, two significant inequalities for the Hilfer fractional derivative of a function in the space ACγ([0,b],Rn), 0≤γ≤1 are obtained. We first verified the extremum principle for the Hilfer fractional derivative. In addition, we estimated the Hilfer derivative of a function at its extreme points. Furthermore, we derived and proved a maximum principle for a nonlinear Hilfer fractional differential equation. Finally, we analyzed the solutions of a nonlinear Hilfer fractional differential equation. Our results generalize and extend some obtained theorems on this topic.

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Section: Introductionmentioning

confidence: 99%

Maximum Principle for Nonlinear Fractional Differential Equations with the Hilfer Derivative

Elbukhari

Fan

2023

Fractal Fract

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“…They examined the dynamics of fractional HIV infection in T-cells as well as the impact of treatment. Thirumalai et al [ 15 ] investigated the fractional order differential equations to analyse the combination of drug treatments for HIV infection. AlShamrani [ 16 ] suggested and evaluated an adaptive immune response model for HIV infection.…”

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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“…Huang et al [19] gave the hierarchical Bayesian inference for HIV dynamic differential equation models which incorporated multiple treatment factors. Thirumalai et al [20] proposed the fractional differential equations based method to analyze the combined drug therapy for HIV infection. Leander et al [21] used the stochastic differential equations to analyze the mixed effects involved in pharmacokinetic data of nicotinic acid.…”

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confidence: 99%

Drug Treatment Effect Model Based on MODWT and Hawkes Self-Exciting Point Process

Nie

Zhao

2022

Computational and Mathematical Methods in Medicine

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In precision medicine, especially in the pharmacodynamic area, the lack of an adequate long-term drug effect monitoring model leads to a quite low robustness to the instant drug treatment. Modelling the effect of drug based on the monitoring variables is essential to measure the drug benefit and its side effect preciously. In order to model the complex drug behavior in the context of time series, a sin function is selected to describe the basic trend of heart rate variable that is medically monitored. A Hawkes self-exciting point process model is chosen to describe the effect caused by multiple and sequential drug usage at different time points. The model considers the time lag between the drug given time and the drug effect during the whole drug emission period. A cumulative Gamma distribution is employed to describe the time lag effect. Simulation results demonstrate the established model effectively when describing the baseline trend and the drug effect with low noise levels, where the maximal overlap discrete wavelet transformation is utilized for the information decomposition in the frequency zone. The real data of the variables heart rate and drug liquemin from a medical database is analyzed. Instead of the original time series, scale variable s4 is selected according to the Granger cointegration test. The results show that the model accurately characterizes the cumulative drug effect with the Pearson correlation test value as 0.22, which is more significant for the value under 0.1. In the future, the model can be extended to more complicated scenarios through taking into account multiple monitoring variables and different kinds of drugs.

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Spectral solutions of fractional differential equations modelling combined drug therapy for HIV infection

Cited by 9 publications

References 20 publications

Maximum Principle for Nonlinear Fractional Differential Equations with the Hilfer Derivative

Maximum Principle for Nonlinear Fractional Differential Equations with the Hilfer Derivative

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

Drug Treatment Effect Model Based on MODWT and Hawkes Self-Exciting Point Process

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