An Optimal Control Approach to HIV Immunology

Arruda, Edilson F.; Dias, Claudia Mazza; Magalhães, Camila Vianna de; Pastore, Dayse Haime; Thomé, Roberto Carlos Antunes; Yang, Hyun Mo

doi:10.4236/am.2015.66102

Cited by 21 publications

(26 citation statements)

References 17 publications

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“…by applying the inverse Laplace transform to both sides of above equations. We computed the first three terms: Table 1 is parameter which used in the model and given in (Arruda et al, 2015) …”

Section: The Laplace-adomian Decomposition Methodsmentioning

confidence: 99%

“…Arbitrary order derivatives are powerful tools for the discretion of the dynamical behavior of various biomaterial and systems. The most iterating feature of these models is their global (nonlocal) characteristics which do not exist in the classical order models (Arruda et al, 2015).…”

Section: *Humanmentioning

confidence: 99%

“…The disease-free equilibrium 0 is locally asymptotically stable if 0 < 1 and is unstable otherwise (Arruda et al, 2015).…”

Section: Theorem 41mentioning

confidence: 99%

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Dynamical behavior of HIV immunology model with non-integer time fractional derivatives

Ashraf

2018

Int. j. adv. appl. sci.

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This paper introduces a mathematical model which describes the dynamics of the spread of HIV in the human body. Human immunodeficiency virus infection destroys the body immune system, increases the risk of certain pathologies, damages body organs such as the brain, kidney and heart or cause the death. Unfortunately, this infection disease currently has no cure to control the diseases. We propose a fractional order model in this paper to describe the dynamics of human immunodeficiency virus (HIV) infection. The Caputo fractional derivative operator of order ∈ (0,1] is employed to obtain the system of fractional differential equations. The basic reproductive number is derived for a general viral production rate which determines the local stability of the infection free equilibrium. The solution of the time fractional model has been procured by employing Laplace Adomian decomposition method (LADM) and the accuracy of the scheme is presented by convergence analysis Moreover, numerical simulation are performed to study the dynamical behavior of solution of the models. Simulations of different epidemiological classes at the effect of the fractional parameters revealed that most undergoing treatment join the recovered class. The results show the both viral production rate and death rate of infected cells play an important role the disease in the society.

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Section: The Laplace-adomian Decomposition Methodsmentioning

confidence: 99%

Section: *Humanmentioning

confidence: 99%

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Dynamical behavior of HIV immunology model with non-integer time fractional derivatives

Ashraf

2018

Int. j. adv. appl. sci.

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“…Based on the above discussions, a simplified model regarding to the HIV infection was presented in [1]. The model is the following set of ordinary differential equations:…”

Section: Modellingmentioning

confidence: 99%

“…Indeed, a novel feature of the present work is the introduction of a variable to represent the CD8+ T cells. Such a variable is extremely important to the model, since it enables the decision maker to evaluate the interaction between the CD8+ T cells, CTL and the other variables in the model, such as the virus load [1].…”

Section: Introductionmentioning

confidence: 99%

An Optimal Control Strategy for HIV Treatment

Arruda¹,

Dias²,

Pastore³

et al. 2016

Proceeding Series of the Brazilian Society of Computational and Applied Mathematics

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Abstract. Considering a simple model that describes the spread of HIV in the human body, this work proposes a strategy to minimize the side effects of medication by introducing control variables that represent the evolution of the medication levels with time. The strategy corresponds to an optimization problem with respect to a prescribed performance function. For a given performance function, an optimal medication strategy is obtained by means of Pontryagin's maximum principle. To solve the set of nonlinear ordinary differential equations that describe the dynamics of susceptible, infected, active cells and HIV, we make use of finite difference method.

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Time-Adaptive Determination of Drug Efficacy in Mathematical Model of HIV Infection

Beilina

Eriksson

Гайнова

2021

Differ Equ Dyn Syst

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The paper considers a time-adaptive finite element method for determination of drug efficacy in a parameter identification problem (PIP) for a system of ordinary differential equations (ODE) that describes dynamics of the primary human immunodeficiency virus (HIV) infection with drug therapy. Tikhonov’s regularization method, optimization approach and finite element method to solve this problem are presented. A posteriori error estimates in the Tikhonov’s functional and reconstructed parameter are derived. Based on these estimates a time adaptive algorithm is formulated and numerically tested for different scenarios of noisy observations of virus population function. Numerical results show a significant improvement of reconstruction of drug efficacy parameter using the local time-adaptive mesh refinement method compared to the gradient method applied on a uniform time mesh.

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An Optimal Control Approach to HIV Immunology

Cited by 21 publications

References 17 publications

Dynamical behavior of HIV immunology model with non-integer time fractional derivatives

Dynamical behavior of HIV immunology model with non-integer time fractional derivatives

An Optimal Control Strategy for HIV Treatment

Time-Adaptive Determination of Drug Efficacy in Mathematical Model of HIV Infection

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