Electron. J. Diff. Equ., Vol. 2015 (2015), No. 50, pp. 1-14.

Optimal control of an SIR model with changing behavior through an education campaign

Hem Raj Joshi, Suzanne Lenhart, Sanjukta Hota, Folashade Agusto

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
Suzanne Lenhart
Dept. of Mathematics
University of Tennessee
Knoxville, TN 37996-1320, USA
email: lenhart@math.utk.edu
Sanjukta Hota
Dept. of Mathematics and Computer Science
Fisk University
Nashville, TN 37208, USA
email: sanjuktahota@gmail.com
Folashade Agusto
Dept. of Mathematics and Statistics
Austin Peay State University
Clarksville, TN 37044, USA
email: fbagusto@gmail.com

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