# American Institute of Mathematical Sciences

2011, 2011(Special): 981-990. doi: 10.3934/proc.2011.2011.981

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

 1 Department of Mathematics and Statistics, Southern Illinois University Edwardsville, Edwardsville, IL 62026 2 Dept. of Electrical and Systems Engineering, Washington University, St. Louis, Missouri, 63130-4899

Received  July 2010 Revised  August 2011 Published  October 2011

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.
Citation: Urszula Ledzewicz, Heinz Schättler. On optimal singular controls for a general SIR-model with vaccination and treatment. Conference Publications, 2011, 2011 (Special) : 981-990. doi: 10.3934/proc.2011.2011.981
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