Optimal Control of Multiple Transmission of Water-Borne Diseases

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 pathwa...

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Bibliographic Details
Published in:International Journal of Mathematics and Mathematical Sciences 2012, Vol.2012 (2012), p.943-958-063
Main Authors: Devipriya, G., Kalaivani, K.
Format: Article
Language:English
Subjects:
Bacteria
Budgets
Climate change
Disease
Drinking water
Drugs
Freshwater resources
Mathematical analysis
Mathematical models
Matlab
Nonlinearity
Optimal control
Pathogens
Retarding
Studies
Substance abuse treatment
Surface water
Tropical diseases
Water quality
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Summary: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.
ISSN:0161-1712
1687-0425
DOI:10.1155/2012/421419