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

Miniak-Górecka Alicja; Nowakowski Andrzej; Miniak-Górecka Alicja; Nowakowski Andrzej

doi:10.3934/mbe.2017017

Mathematical Biosciences and Engineering

2017, Volume 14, Issue 1: 263-275. doi: 10.3934/mbe.2017017

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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

Received: 22 October 2015 Accepted: 22 April 2016 Published: 01 January 2017
MSC : Primary: 49J23; Secondary: 35K57

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.
- 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[J]. Mathematical Biosciences and Engineering, 2017, 14(1): 263-275. doi: 10.3934/mbe.2017017

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Abstract

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.

References

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