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Optimal Strategies for Psoriasis Treatment
- 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