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A SEIR model for control of infectious diseases with constraints. (English) Zbl 1327.92055

Summary: Optimal control can be of help to test and compare different vaccination strategies of a certain disease. In this paper we propose the introduction of constraints involving state variables on an optimal control problem applied to a compartmental SEIR (susceptible, exposed, infectious and recovered) model. We study the solution of such problems when mixed state control constraints are used to impose upper bounds on the available vaccines at each instant of time. We also explore the possibility of imposing upper bounds on the number of susceptible individuals with and without limitations on the number of vaccines available. In the case of mere mixed constraints a numerical and analytical study is conducted while in the other two situations only numerical results are presented.

MSC:

92D30 Epidemiology
49K15 Optimality conditions for problems involving ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems

Software:

ICLOCS; Ipopt
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References:

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