An optimal control approach to cancer treatment under immunological activity

Volume 38 / 2011

Urszula Ledzewicz, Mohammad Naghnaeian, Heinz Schättler Applicationes Mathematicae 38 (2011), 17-31 MSC: 49K15, 92C50. DOI: 10.4064/am38-1-2


Mathematical models for cancer treatment that include immunological activity are considered as an optimal control problem with an objective that is motivated by a separatrix of the uncontrolled system. For various growth models on the cancer cells the existence and optimality of singular controls is investigated. For a Gompertzian growth function a synthesis of controls that move the state into the region of attraction of a benign equilibrium point is developed.


  • Urszula LedzewiczDepartment of Mathematics and Statistics
    Southern Illinois University Edwardsville
    Edwardsville, IL 62026-1653, U.S.A.
  • Mohammad NaghnaeianDepartment of Mathematics and Statistics
    Southern Illinois University at Edwardsville
    Edwardsville, IL, 62026-1653, U.S.A.
  • Heinz SchättlerDepartment of Electrical and
    Systems Engineering
    Washington University
    St. Louis, MO 63130-4899, U.S.A.

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