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Optimal Strategies for Psoriasis Treatment

Authors :
Ellina Grigorieva
Evgenii Khailov
Source :
Mathematical and Computational Applications, Vol 23, Iss 3, p 45 (2018)
Publication Year :
2018
Publisher :
MDPI AG, 2018.

Abstract

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.

Details

Language :
English
ISSN :
22978747
Volume :
23
Issue :
3
Database :
Directory of Open Access Journals
Journal :
Mathematical and Computational Applications
Publication Type :
Academic Journal
Accession number :
edsdoj.f9c2b4e63be4c5a8f19b2bb08379cfc
Document Type :
article
Full Text :
https://doi.org/10.3390/mca23030045