In this thesis, we formulate an optimal control problem for an SIR model with timevarying population. Vaccination and treatment are considered as control variables to manage the outbreak of a disease. We studied Pontryagin’s maximum principle to characterize the optimal levels of the two controls. The results show that the optimal vaccination schedule can be singular whereas for the optimal treatment schedules bang-bang control is the optimal strategy.
|Advisor:||Ledzewicz, Urszula, Schaettler, Heinz|
|Commitee:||Chew, Song Foh, Parish, James L.|
|School:||Southern Illinois University at Edwardsville|
|Department:||Mathematics and Statistics|
|School Location:||United States -- Illinois|
|Source:||MAI 56/01M(E), Masters Abstracts International|
|Keywords:||Bang-bang control, Epidemiology, Optimal control, Pontryagin maximum principle, Singular control, Sir model|
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