American Institute of Mathematical Sciences

Advanced
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

Urszula Ledzewicz 1, and  Heinz Schättler 2,

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