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Optimal Strategies for Psoriasis Treatment

TWU Department of Mathematics and Computer Science, Texas Woman’s University, Denton, TX 76204, USA
MSU Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, Moscow 119992, Russia
Author to whom correspondence should be addressed.
Math. Comput. Appl. 2018, 23(3), 45;
Received: 1 August 2018 / Revised: 31 August 2018 / Accepted: 31 August 2018 / Published: 4 September 2018
(This article belongs to the Special Issue Optimization in Control Applications)
Within a given time interval we consider a nonlinear system of differential equations describing psoriasis treatment. Its phase variables define the concentrations of T-lymphocytes, keratinocytes and dendritic cells. Two scalar bounded controls are introduced into this system to reflect medication dosages aimed at suppressing interactions between T-lymphocytes and keratinocytes, and between T-lymphocytes and dendritic cells. For such a controlled system, a minimization problem of the concentration of keratinocytes at the terminal time is considered. For its analysis, the Pontryagin maximum principle is applied. As a result of this analysis, the properties of the optimal controls and their possible types are established. It is shown that each of these controls is either a bang-bang type on the entire time interval or (in addition to bang-bang type) contains a singular arc. The obtained analytical results are confirmed by numerical calculations using the software “BOCOP-2.0.5”. Their detailed analysis and the corresponding conclusions are presented. View Full-Text
Keywords: psoriasis; nonlinear control system; optimal control; Pontryagin maximum principle; switching function; Lie brackets; singular arc; chattering control psoriasis; nonlinear control system; optimal control; Pontryagin maximum principle; switching function; Lie brackets; singular arc; chattering control
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MDPI and ACS Style

Grigorieva, E.; Khailov, E. Optimal Strategies for Psoriasis Treatment. Math. Comput. Appl. 2018, 23, 45.

AMA Style

Grigorieva E, Khailov E. Optimal Strategies for Psoriasis Treatment. Mathematical and Computational Applications. 2018; 23(3):45.

Chicago/Turabian Style

Grigorieva, Ellina, and Evgenii Khailov. 2018. "Optimal Strategies for Psoriasis Treatment" Mathematical and Computational Applications 23, no. 3: 45.

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