Control of the HIV infection and drug dosage

Mhawej, Marie-José; Moog, Claude H.; Biafore, Federico L.; Brunet-François, Cécile

doi:10.1016/j.bspc.2009.05.001

Cited by 43 publications

(54 citation statements)

References 22 publications

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“…In this regard the stability analysis is investigated in [16], [17], [25], [26], [28] and [30], and a variety of control strategies is applied to HIV-1. For instance, feedback control in [7]- [9] and [20], nonlinear theory based control in [14]- [15] and [29], model predictive control in [18], [27], optimal control in [10] [22] [31] [32] and [36] and intelligent control in [59] [63] can be noticed.…”

Section: On the Other Hand Recent Years Have Witnessed Growing Interementioning

confidence: 99%

Modeling and stability analysis of HIV-1 as a time delay fuzzy T–S system via LMIs

Abbasi

Beheshti

Mohraz

2015

Applied Mathematical Modelling

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Section: On the Other Hand Recent Years Have Witnessed Growing Interementioning

confidence: 99%

Modeling and stability analysis of HIV-1 as a time delay fuzzy T–S system via LMIs

Abbasi

Beheshti

Mohraz

2015

Applied Mathematical Modelling

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“…A number of authors have applied techniques from nonlinear control to this problem, but in general the explicit link between the drug dose and the physiological effect, via the PK, is neglected so that the controls derived are continuous in time. In the finite-deminsional case, Mhawej et al [13] addressed this control problem via feedback linearization applied to a PD model of HIV dynamics. A single-compartment PK model was then used to estimate a dosing regime that gave rise to the required continuous control law.…”

Section: Application: Control Of Viral Load In Hivmentioning

confidence: 99%

“…The general control problem associated with models of this form is to choose daily dosages in order to reduce viral load a certain amount in the short-term and then below a detectability limit in the medium to long-term (see, for example, [13]). Therefore, consider the problem of determining doses D i (i = 1, .…”

Section: Application: Control Of Viral Load In Hivmentioning

confidence: 99%

Controlling Nonlinear Infinite-Dimensional Systems via the Initial State

Evans¹

2013

SIAM J. Control Optim.

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Abstract. A control problem is considered for nonlinear time-varying systems described by partial differential equations, in which the control acts only via part of the initial state. The problem is to drive part, or all, of the process to some desired state in a specified time. The motivation for such systems are control problems arising in medicine and biology that involve spatial or age characteristics, or time-delays. The approach taken is to formulate the problem as a fixed point problem for a suitable abstract differential equation and then apply a version of the Contraction Mapping Theorem. Conditions are imposed so that the problem is well defined and a weaker form of solution exists. The solution obtained ensures that the target state is achieved on the range of a linear operator arising from a linearisation of the system about an initial estimate for the control. Although the Contraction Mapping Theorem yields a constructive method to determine the solution an alternative, more direct, approach is presented, which relies on an iterative scheme for the control and the original dynamics.

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“…Meanwhile the parameter estimations in [10] have been made based on the pretreatment and posttreatment data of six volunteer patients. From the study in [10], based on the pretreatment data, theβ median value is estimated to be 9.34 × 10 −7 (ml / day). Table I presents the estimated value of λ for HIV-infected patients.…”

Section: A Three-dimensional Hiv Dynamicsmentioning

confidence: 99%