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Nominal and neighboring-optimal control approaches to the adoptive immunotherapy for cancer

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Abstract

In this work, a nominal-plus-neighboring-optimal control approach is suggested for the treatment of cancer using the adoptive cellular immunotherapy. The main goal of this therapy is to minimize both tumor concentration and treatment costs while restoring natural defense mechanisms and activating immune response. In the presence of an additional initial concentration of cancer cells, the biological effects of the introduction of a neighboring-optimal treatment in addition to the existing nominally therapy are explored and investigated. The optimal control problem is presented by defining appropriate objective functions. The Pontryagin’s maximum principle and the Pontryagin procedure are both used to obtain optimal solutions for subsequently providing nominal and neighboring-optimal control configurations. The optimal systems are derived and solved numerically using an adapted iterative method with a Runge–Kutta fourth order scheme.

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Acknowledgments

The authors would like to thank the Editor in Chief and all anonymous referees for their valuable comments.

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Authors and Affiliations

  1. Department of Mathematics and Computer Sciences, Faculty of Sciences Ben M’Sik, Hassan II University, Avenue Commandant Driss Elharti, P.O. Box 7955, Casablanca, Morocco

    Amine Hamdache, Smahane Saadi & Ilias Elmouki

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  1. Amine Hamdache
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  3. Ilias Elmouki
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Correspondence to Ilias Elmouki.

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Hamdache, A., Saadi, S. & Elmouki, I. Nominal and neighboring-optimal control approaches to the adoptive immunotherapy for cancer. Int. J. Dynam. Control 4, 346–361 (2016). https://doi.org/10.1007/s40435-015-0205-y

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