Modelling of Hiv Infection: Vaccine Readiness, Drug Effectiveness and Therapeutical Failures

Xia, Xiaohua

doi:10.3182/20060402-4-br-2902.00485

Cited by 6 publications

(14 citation statements)

References 24 publications

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“…−→ ∅ (13) Using reactions (1)-(13), we obtain the following model; (14) will be conducted using MATLAB. Parameters and initial conditions were obtained from previous works in the area Perelson [1999], Xia [2007], Conejeros et al [2007]. Using clinical data for the CD4+T cell counts Greenough [2000], Fauci et al [1996], some parameters were adjusted, see Table 1, in order to obtain the best match with clinical data.…”

Section: Virus Proliferationmentioning

confidence: 99%

Towards Modeling HIV Long Term Behavior

Hernandez‐Vargas

Mehta

Middleton

2011

IFAC Proceedings Volumes

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The precise mechanism that causes HIV infection to progress to AIDS is still unknown. This paper presents a mathematical model which is able to predict the entire trajectory of the HIV/AIDS dynamics, then a possible explanation for this progression is examined. A dynamical analysis of this model reveals a set of parameters which may produce two real equilibria in the model. One equilibrium is stable and represents those individuals who have been living with HIV for at least 7 to 9 years, and do not develop AIDS. The other one is unstable and represents those patients who developed AIDS in an average period of 10 years. However, further work is needed since the proposed model is sensitive to parameter variations.

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Section: Virus Proliferationmentioning

confidence: 99%

Towards Modeling HIV Long Term Behavior

Hernandez‐Vargas

Mehta

Middleton

2011

IFAC Proceedings Volumes

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“…Notice that, sinceÃ i is a Schur matrix, −Ã i + I is an M-matrix, whose inverse is a positive matrix, so that the vectors i in (39) are positive. The control rule (39) guarantees an upper bound on the cost function, i.e.…”

Section: Simulation Resultsmentioning

confidence: 99%

“…Note that typically during the treatment of HIV, clinical visits have a frequency of once a month or less. Using the parameter values of Table I and the control rule in (39), we see in Figure 3 that for an initial period of time, the switching rule maintains a low wild-type concentration and suppresses the concentrations of genotypes 1 and 2. However, the highly resistant genotype eventually grows since none of the therapies affect this genotype.…”

Section: Simulation Resultsmentioning

confidence: 99%

“…Several mathematical models have been proposed to describe HIV dynamics since 1990. Most of the models present a basic relationship between immune system cells; CD4 + T cells that are one of the main targets of the virus, macrophages cells that constitute an alternate target for HIV replication, infected cells and virus [36][37][38][39][40]. These models used different mechanisms to explain HIV infection dynamics; however, for this paper we are just interested in the virus mutation treatment problem.…”

Section: Application To a Mathematical Model Of Virus Mutation Treatmentmentioning

confidence: 99%

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Discrete‐time control for switched positive systems with application to mitigating viral escape

Hernandez‐Vargas

Colaneri

Middleton

et al. 2011

Intl J Robust & Nonlinear

334

161

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SUMMARYThis paper has been motivated by the problem of viral mutation in HIV infection. Under simplifying assumptions, viral mutation treatment dynamics can be viewed as a positive switched linear system. Using linear co-positive Lyapunov functions, results for the synthesis of stabilizing, guaranteed performance and optimal control laws for switched linear systems are presented. These results are then applied to a simplified human immunodeficiency viral mutation model. The optimal switching control law is compared with the law obtained through an easily computable guaranteed cost function. Simulation results show the effectiveness of these methods.

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“…2) It can be seen that a model of such a simple nature is able to adequately reflect the disease progression from the initial infection to an asymptomatic stage after the set-point is reached (See [9]).…”

Section: Properties Of Hiv Basic Modelmentioning

confidence: 99%

Optimal Control Strategy for a Fully Determined HIV Model

Shirazian

Farahi

2010

ICA

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This paper shows how mathematical methods can be implemented to formulate guidelines for clinical testing and monitoring of HIV/AIDS disease. First, a mathematical model for HIV infection is presented which the measurement of the CD4+T cells and the viral load counts are needed to estimate all its parameters. Next, through an analysis of model properties, the minimal number of measurement samples is obtained. In the sequel, the effect of Reverse Transcriptase enzyme Inhibitor (RTI) on HIV progression is demonstrated by using a control function. Also the total cost of treatment by this kind of drugs has been minimized. The numerical results are obtained by a numerical method in discretization issue, called AVK

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Modelling of Hiv Infection: Vaccine Readiness, Drug Effectiveness and Therapeutical Failures

Cited by 6 publications

References 24 publications

Towards Modeling HIV Long Term Behavior

Towards Modeling HIV Long Term Behavior

Discrete‐time control for switched positive systems with application to mitigating viral escape

Optimal Control Strategy for a Fully Determined HIV Model

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