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On application of optimal control to SEIR normalized models: Pros and cons

1. SYSTEC, DEEC, Faculdade de Engenharia da Universidade do Porto, Rua Dr. Roberto Frias, 4200–465 Porto, Portugal
2. CTAC, Departamento de Engenharia Civil, Universidade do Minho, Campus de Gualtar, 4710-057 Braga, Portugal

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In this work we normalize a SEIR model that incorporates exponential natural birth and death, as well as disease-caused death. We use optimal control to control by vaccination the spread of a generic infectious disease described by a normalized model with $L^1$ cost. We discuss the pros and cons of SEIR normalized models when compared with classical models when optimal control with $L^1$ costs are considered. Our discussion highlights the role of the cost. Additionally, we partially validate our numerical solutions for our optimal control problem with normalized models using the Maximum Principle.

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Citation: Maria do Rosário de Pinho, Filipa Nunes Nogueira. On application of optimal control to SEIR normalized models: Pros and cons. Mathematical Biosciences and Engineering, 2017, 14(1): 111-126. doi: 10.3934/mbe.2017008

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