Vol. 9, No. 1, 2016

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Investigating cholera using an SIR model with age-class structure and optimal control

K. Renee Fister, Holly Gaff, Elsa Schaefer, Glenna Buford and Bryce C. Norris

Vol. 9 (2016), No. 1, 83–100

The use of systems of differential equations in mathematical modeling in conjunction with epidemiology continues to be an area of focused research. This paper briefly acquaints readers with epidemiology, cholera, and the need for effective control strategies; discusses cholera dynamics through a variation on the SIR epidemiological model in which two separate age classes exist in a population; finds the numeric value for R0 to be approximately 1.54 using estimated parameters for Bangladesh; and employs an optimal control resulting in a suggestion that a protection control be implemented at the end of the monsoon season.

endemic cholera, SIR model, age class structure, ordinary differential equations, optimal control
Mathematical Subject Classification 2010
Primary: 35L45, 35L50, 92D30
Received: 7 January 2014
Revised: 7 December 2014
Accepted: 27 December 2014
Published: 17 December 2015

Communicated by Suzanne Lenhart
K. Renee Fister
Department of Mathematics and Statistics
Murray State University
Murray, KY 42071
United States
Holly Gaff
Department of Biological Sciences
Old Dominion University
Norfolk, VA 23529
United States
Elsa Schaefer
Department of Mathematics
Marymount University
Arlington, VA 22207
United States
Glenna Buford
Wooga GmbH
Bryce C. Norris
Department of Mathematics and Statistics
Murray State University
Murray, KY 42071
United States