Open AccessOptimal Control of Multiple Transmission of Water-Borne Diseases
Author(s) -
G. Devipriya,
K. Kalaivani
Publication year - 2012
Publication title -
international journal of mathematics and mathematical sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 39
eISSN - 1687-0425
pISSN - 0161-1712
DOI - 10.1155/2012/421419
Subject(s) - mathematics , ode , nonlinear system , transmission (telecommunications) , control theory (sociology) , optimal control , mathematical optimization , matlab , transversality , control (management) , mathematical analysis , computer science , artificial intelligence , telecommunications , physics , quantum mechanics , operating system
A controlled SIWR model was considered which was an extension of the simple SIR model by adjoining a compartment () 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 functionis 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
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