CONTROLO’2014 – Proceedings of the 11th Portuguese Conference on Automatic Control pp 135-145 | Cite as
Optimal Control of a SEIR Model with Mixed Constraints and L1 Cost
Abstract
Optimal control can help to determine vaccination policies for infectious diseases. For diseases transmitted horizontally, SEIR compartment models have been used. Most of the literature on SEIR models deals with cost functions that are quadratic with respect to the control variable, the rate of vaccination. Here, we propose the introduction of a cost of L 1 type which is linear with respect to the control variable. Our starting point is the recent work [1], where the number of vaccines at each time is assumed to be limited. This yields an optimal control problem with a mixed control-state constraint. We discuss the necessary optimality conditions of the Maximum Principle and present numerical solutions that precisely satisfy the necessary conditions.
Keywords
optimal control epidemiology mixed constraints numerical solutions bang-bang controlPreview
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