Open AccessSufficient optimality conditions for a class of epidemic problems with control on the boundary
Author(s) -
Alicja Miniak-Górecka,
Andrzej Nowakowski
Publication year - 2017
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2017017
Subject(s) - mathematics , optimal control , boundary (topology) , operator (biology) , class (philosophy) , dual (grammatical number) , dynamic programming , mathematical optimization , boundary value problem , optimality criterion , type (biology) , mathematical analysis , computer science , art , biochemistry , chemistry , ecology , literature , repressor , artificial intelligence , biology , transcription factor , gene
In earlier paper of V. Capasso et al it is considered a simply model of controlling an epidemic, which is described by three functionals and systems of two PDE equations having the feedback operator on the boundary. Necessary optimality conditions and two gradient-type algorithms are derived. This paper constructs dual dynamic programming method to derive sufficient optimality conditions for optimal solution as well ε-optimality conditions in terms of dual dynamic inequalities. Approximate optimality and numerical calculations are presented too.