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Sufficient optimality conditions for a class of epidemic problems with control on the boundary

. Faculty of Math and Computer Sciences, University of Lodz, Banacha 22, 90-238 Lodz, Poland

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 $\varepsilon $-optimality conditions in terms of dual dynamic inequalities. Approximate optimality and numerical calculations are presented too.

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Keywords Sufficient optimality conditions; dual dynamic programming; dual dynamic programming; epidemic problem; parabolic equation

Citation: Miniak-Górecka Alicja, Nowakowski Andrzej. Sufficient optimality conditions for a class of epidemic problems with control on the boundary. Mathematical Biosciences and Engineering, 2017, 14(1): 263-275. doi: 10.3934/mbe.2017017


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Copyright Info: 2017, Miniak-Górecka Alicja, et al., licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

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