#### 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
##### Abstract

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 ${R}_{0}$ 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.

##### Keywords
endemic cholera, SIR model, age class structure, ordinary differential equations, optimal control
##### Mathematical Subject Classification 2010
Primary: 35L45, 35L50, 92D30