Optimal control of the chemotherapy of HIV

Kirschner, Denise E.; Lenhart, Suzanne; Serbin, S.

doi:10.1007/s002850050076

Cited by 427 publications

(334 citation statements)

References 22 publications

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“…Standard techniques in optimal control, Hamiltonian and Pontryagin's Maximum Principles, are applied to derive the optimal solution and the problem is solved numerically for several scenarios. In Kirschner et al [15] the objective is to minimize the systematic cost of chemotherapy in early HIV treatment. The interaction of the immune system with HIV is described by an ODE model.…”

Section: Introductionmentioning

confidence: 99%

Controlling the number of HIV infectives in a mobile population

Sani

Kroese

2008

Mathematical Biosciences

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Abstract. The spread of the human immunodeficiency virus (HIV) depends prominently on the migration of people between different regions. An important consequence of this population mobility is that HIV control strategies that are optimal in a regional sense may not be optimal in a national sense. We formulate various mathematical control problems for HIV spread in mobile heterosexual populations, and show how optimal regional control strategies can be obtained that minimize the national spread of HIV. We apply the cross-entropy method to solve these highly multi-modal and non-linear optimization problems. We demonstrate the effectiveness of the method via a range of experiments and illustrate how the form of the optimal control function depends on the mathematical model used for the HIV spread.

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Section: Introductionmentioning

confidence: 99%

Controlling the number of HIV infectives in a mobile population

Sani

Kroese

2008

Mathematical Biosciences

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“…For example, Kirschner, Lenhart, and Serbin (Ref. 8) consider an optimal control problem for chemotherapy of HIV which accounts for latently and actively infected CD4 + T-cells; Fister and Panetta (Ref. 9) analyze a mathematical model which takes into account bone marrow destruction.…”

Section: Introductionmentioning

confidence: 99%

Optimal Bang-Bang Controls for a Two-Compartment Model in Cancer Chemotherapy

Ledzewicz

Schättler

2002

Journal of Optimization Theory and Applications

158

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Abstract.A class of mathematical models for cancer chemotherapy which have been described in the literature take the form of an optimal control problem over a finite horizon with control constraints and dynamics given by a bilinear system. In this paper, we analyze a twodimensional model in which the cell cycle is broken into two compartments. The cytostatic agent used as control to kill the cancer cells is active only in the second compartment where cell division occurs and the cumulative effect of the drug is used to model the negative effect of the treatment on healthy cells. It is shown that singular controls are not optimal for this model and the optimality properties of bang-bang controls are established. Specifically, transversality conditions at the switching surfaces are derived. In a nondegenerate setting, these conditions guarantee the local optimality of the flow if satisfied, while trajectories will be no longer optimal if they are violated.

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“…The combined short and long period treatment schemes aims at providing a standard and effective treatment in the attack phase and, after the improvement of the patient's condition, a maintenance treatment based on optimized doses that has less side-effects yet keeps the health condition in a clinically satisfactory region. In the previous results by the authors, the original non-linear model was used to compute the optimal strategy for the whole control horizon (see, for instance, Caetano and Yoneyama 1999b, Felippe de Souza et al 2000, Kirschner and Webb 1996and Kirschner et al 1997). However, it was very difficult to extend them for computing long term treatment schemes.…”

Section: Discussionmentioning

confidence: 99%

Short and long period optimization of drug doses in the treatment of AIDS

Caetano

Yoneyama

2002

An. Acad. Bras. Ciênc.

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Numerical optimization techniques are useful in solving problems of computing the best inputs for systems described by mathematical models and when the objectives can be stated in a quantitative form. This work concerns the problem of optimizing the drug doses in the treatment of AIDS in terms of achieving a balance between the therapeutic response and the side effects. A mathematical model describing the dynamics of HIV viruses and CD4 cells is used to compute the short term optimal drug doses in the treatments of patients with AIDS by a direct method of optimization using a cost function of Bolza type. The model parameters were fitted to actual published clinical data. In order to simplify the numerical procedures, the control law is expressed as a series and the sub-optimal control is obtained by truncating the higher terms. When the patient reaches a clinically satisfactory state, the LQR -Linear Quadratic Regulator technique is used to determine the long period maintenance doses for the drugs. The doses computed using the LQR technique tend to be smaller than equivalent constant-dose therapy in terms of increase in the counts of CD4 + T cells and reduction of the density of free viruses.

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Optimal control of the chemotherapy of HIV

Cited by 427 publications

References 22 publications

Controlling the number of HIV infectives in a mobile population

Controlling the number of HIV infectives in a mobile population

Optimal Bang-Bang Controls for a Two-Compartment Model in Cancer Chemotherapy

Short and long period optimization of drug doses in the treatment of AIDS

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