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On application of optimal control to SEIR normalized models: pros and cons. (English) Zbl 1351.49054

Summary: 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.

MSC:

49N90 Applications of optimal control and differential games
49K15 Optimality conditions for problems involving ordinary differential equations
49J15 Existence theories for optimal control problems involving ordinary differential equations
49M37 Numerical methods based on nonlinear programming
92C60 Medical epidemiology
92D30 Epidemiology

Software:

Ipopt; AMPL; WORHP
PDFBibTeX XMLCite
Full Text: DOI

References:

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