Geodesic
An optimal control approach to cancer treatment under immunological activity
Urszula Ledzewicz1 ; Mohammad Naghnaeian2 ; Heinz Schättler3
1 Department of Mathematics and Statistics Southern Illinois University Edwardsville Edwardsville, IL 62026-1653, U.S.A.
2 Department of Mathematics and Statistics Southern Illinois University at Edwardsville Edwardsville, IL, 62026-1653, U.S.A.
3 Department of Electrical and Systems Engineering Washington University St. Louis, MO 63130-4899, U.S.A.
Applicationes Mathematicae, Tome 38 (2011) no. 1, pp. 17-31 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/am38-1-2
Keywords: mathematical models cancer treatment include immunological activity considered optimal control problem objective motivated separatrix uncontrolled system various growth models cancer cells existence optimality singular controls investigated gompertzian growth function synthesis controls move state region attraction benign equilibrium point developed

Urszula Ledzewicz 1 ; Mohammad Naghnaeian 2 ; Heinz Schättler 3

1 Department of Mathematics and Statistics Southern Illinois University Edwardsville Edwardsville, IL 62026-1653, U.S.A.
2 Department of Mathematics and Statistics Southern Illinois University at Edwardsville Edwardsville, IL, 62026-1653, U.S.A.
3 Department of Electrical and Systems Engineering Washington University St. Louis, MO 63130-4899, U.S.A. 
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Urszula Ledzewicz; Mohammad Naghnaeian; Heinz Schättler. An optimal control approach to cancer treatment under immunological activity. Applicationes Mathematicae, Tome 38 (2011) no. 1, pp. 17-31. doi: 10.4064/am38-1-2

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