Optimal Strategies for Psoriasis Treatment
AbstractWithin 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
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Grigorieva, E.; Khailov, E. Optimal Strategies for Psoriasis Treatment. Math. Comput. Appl. 2018, 23, 45.
Grigorieva E, Khailov E. Optimal Strategies for Psoriasis Treatment. Mathematical and Computational Applications. 2018; 23(3):45.Chicago/Turabian Style
Grigorieva, Ellina; Khailov, Evgenii. 2018. "Optimal Strategies for Psoriasis Treatment." Math. Comput. Appl. 23, no. 3: 45.
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