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On optimal singular controls for a general SIR-model with vaccination and treatment

Pages: 981 - 990, Issue Special, September 2011

 Abstract        Full Text (302.6K)              

Urszula Ledzewicz - Department of Mathematics and Statistics, Southern Illinois University Edwardsville, Edwardsville, IL 62026, United States (email)
Heinz Sch├Ąttler - Dept. of Electrical and Systems Engineering, Washington University, St. Louis, Missouri, 63130-4899, United States (email)

Abstract: A general SIR-model with vaccination and treatment is considered as a multi-input optimal control problem over a xed time horizon. Existence and local optimality of singular controls is investigated. It is shown that the optimal vaccination schedule can be singular, but that treatment schedules are not.

Keywords:  optimal control, epidemiology, SIR-model, singular controls.
Mathematics Subject Classification:  Primary: 49K15; Secondary: 92B05

Received: July 2010;      Revised: August 2011;      Published: October 2011.