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On the Role of the Objective in the Optimization of Compartmental Models for Biomedical Therapies

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Abstract

We review and discuss results obtained through an application of tools of nonlinear optimal control to biomedical problems. We discuss various aspects of the modeling of the dynamics (such as growth and interaction terms), modeling of treatment (including pharmacometrics of the drugs), and give special attention to the choice of the objective functional to be minimized. Indeed, many properties of optimal solutions are predestined by this choice which often is only made casually using some simple ad hoc heuristics. We discuss means to improve this choice by taking into account the underlying biology of the problem.

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Data Availability Statement

All data generated or analyzed during this study are included in this published article.

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Acknowledgements

We are grateful to four anonymous referees of this paper for their useful comments which helped us improve our presentation.

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Authors and Affiliations

  1. Lodz University of Technology, 90-924, Lodz, Poland

    Urszula Ledzewicz

  2. Southern Illinois University Edwardsville, Edwardsville, IL, 62026-1653, USA

    Urszula Ledzewicz

  3. Washington University, St. Louis, MO, 63130, USA

    Heinz Schättler

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  1. Urszula Ledzewicz
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Correspondence to Urszula Ledzewicz.

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Ledzewicz, U., Schättler, H. On the Role of the Objective in the Optimization of Compartmental Models for Biomedical Therapies. J Optim Theory Appl 187, 305–335 (2020). https://doi.org/10.1007/s10957-020-01754-2

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