Hem Raj Joshi, Suzanne Lenhart, Sanjukta Hota, Folashade Agusto
Abstract:
An SIR type model is expanded to include the use of education or information
given to the public as a control to manage a disease outbreak when
effective treatments or vaccines are not readily available or too costly
to be widely used. The information causes a change in behavior resulting in
three susceptible classes. We study stability analysis and use optimal
control theory on the system of differential equations to achieve the goal
of minimizing the infected population (while minimizing the cost).
We illustrate our results with some numerical simulations.
Submitted February 4, 2014. Published February 19, 2015.
Math Subject Classifications: 35K55, 49K20
Key Words: Effect of education on SIR models; optimal control.
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Hem Raj Joshi Dept. of Mathematics and Computer Science Xavier University Cincinnati, OH 45207-4441, USA email: joshi@xavier.edu |
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Suzanne Lenhart Dept. of Mathematics University of Tennessee Knoxville, TN 37996-1320, USA email: lenhart@math.utk.edu |
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Sanjukta Hota Dept. of Mathematics and Computer Science Fisk University Nashville, TN 37208, USA email: sanjuktahota@gmail.com |
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Folashade Agusto Dept. of Mathematics and Statistics Austin Peay State University Clarksville, TN 37044, USA email: fbagusto@gmail.com |
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