International Journal of Mathematics and Mathematical Sciences
Volume 2012 (2012), Article ID 421419, 16 pages
Research Article

Optimal Control of Multiple Transmission of Water-Borne Diseases

P. G. Department of Mathematics, Women's Christian College, Chennai 600006, India

Received 29 March 2012; Accepted 25 May 2012

Academic Editor: B. N. Mandal

Copyright © 2012 G. Devipriya and K. Kalaivani. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A controlled SIWR model was considered which was an extension of the simple SIR model by adjoining a compartment ( 𝑊 ) that tracks the pathogen concentration in the water. New infections arise both through exposure to contaminated water as well as by the classical SIR person-person transmission pathway. The controls represent an immune boosting and pathogen suppressing drugs. The objective function is based on a combination of minimizing the number of infected individuals and the cost of the drugs dose. The optimal control is obtained by solving the optimality system which was composed of four nonlinear ODEs with initial conditions and four nonlinear adjoint ODEs with transversality conditions. The results were analysed and interpreted numerically using MATLAB.