Optimal control applied to vaccination and treatment
strategies for various epidemiological models
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1.
Community and Environmental Health, College of Health Sciences, Old Dominion University, 3133A Technology Building, Norfolk, VA 23529
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2.
Department of Mathematics, Marymount University, 2807 North Glebe Road, Arlington, VA 22207
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Received:
01 February 2008
Accepted:
29 June 2018
Published:
01 June 2009
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MSC :
49K15, 92B05, 34H05.
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Mathematical models provide a powerful tool for investigating the
dynamics and control of infectious diseases, but quantifying the
underlying epidemic structure can be challenging especially for new
and under-studied diseases.
Variations of standard SIR, SIRS, and SEIR epidemiological
models are considered to determine the sensitivity of these models to
various parameter values that may not be fully known when the models are
used to investigate emerging diseases. Optimal control theory is applied
to suggest the most effective mitigation
strategy to minimize the number of individuals who become infected in the
course of an infection while efficiently balancing
vaccination and treatment applied to the models with various cost
scenarios. The optimal control simulations suggest that regardless of the
particular epidemiological structure and of the comparative cost of
mitigation strategies, vaccination, if available, would be a
crucial piece of any intervention plan.
Citation: Holly Gaff, Elsa Schaefer. Optimal control applied to vaccination and treatmentstrategies for various epidemiological models[J]. Mathematical Biosciences and Engineering, 2009, 6(3): 469-492. doi: 10.3934/mbe.2009.6.469
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Abstract
Mathematical models provide a powerful tool for investigating the
dynamics and control of infectious diseases, but quantifying the
underlying epidemic structure can be challenging especially for new
and under-studied diseases.
Variations of standard SIR, SIRS, and SEIR epidemiological
models are considered to determine the sensitivity of these models to
various parameter values that may not be fully known when the models are
used to investigate emerging diseases. Optimal control theory is applied
to suggest the most effective mitigation
strategy to minimize the number of individuals who become infected in the
course of an infection while efficiently balancing
vaccination and treatment applied to the models with various cost
scenarios. The optimal control simulations suggest that regardless of the
particular epidemiological structure and of the comparative cost of
mitigation strategies, vaccination, if available, would be a
crucial piece of any intervention plan.
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