Optimal control and stability analysis of an epidemic model with education campaign and treatment

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

doi:10.3934/proc.2015.0621

Article Contents

2015, Volume 2015: 621-634. Doi: 10.3934/proc.2015.0621 open access

This issue Previous Article Positive solutions of a fractional boundary value problem with a fractional derivative boundary condition Next Article An iterative approach to $L^\infty$-boundedness in quasilinear Keller-Segel systems

Optimal control and stability analysis of an epidemic model with education campaign and treatment

1.
Department of Mathematics and Computer Science, Fisk University, Nashville TN 37208
2.
Department of Ecology and Evolutionary Biology, University of Kansas, Lawrence, KS 66045
3.
Department of Mathematics, Xavier University, Cincinnati, OH 45207-4441
4.
Department of Mathematics, University of Tennessee, Knoxville, TN 37996-1300

Received: August 31, 2014

Revised: August 31, 2015

Published: October 2015

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Abstract

In this paper we investigated a SIR epidemic model in which education campaign and treatment are both important for the disease management. Optimal control theory was used on the system of differential equations to achieve the goal of minimizing the infected population and slow down the epidemic outbreak. Stability analysis of the disease free equilibrium of the system was completed. Numerical results with education campaign levels and treatment rates as controls are illustrated.

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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