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Optimal Control of Multiple Transmission of Water-Borne Diseases

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  • G. Devipriya
  • K. Kalaivani

Abstract

A controlled SIWR model was considered which was an extension of the simple SIR model by adjoining a compartment ( ð ‘Š ) 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.

Suggested Citation

  • G. Devipriya & K. Kalaivani, 2012. "Optimal Control of Multiple Transmission of Water-Borne Diseases," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2012, pages 1-16, July.
    • Handle: RePEc:hin:jijmms:421419
    DOI: 10.1155/2012/421419
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    1. Klein, Eili & Laxminarayan, Ramanan & Smith, David L. & Gilligan, Christopher A., 2007. "Economic incentives and mathematical models of disease," Environment and Development Economics, Cambridge University Press, vol. 12(5), pages 707-732, October.
    2. Goldman, Steven M. & Lightwood, James, 1996. "Cost Optimization in the SIS Model of Infectious Disease with Treatment," Department of Economics, Working Paper Series qt0r88q87t, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
    3. Goldman Steven Marc & Lightwood James, 2002. "Cost Optimization in the SIS Model of Infectious Disease with Treatment," The B.E. Journal of Economic Analysis & Policy, De Gruyter, vol. 2(1), pages 1-24, April.
    4. Mark A. Shannon & Paul W. Bohn & Menachem Elimelech & John G. Georgiadis & Benito J. Mariñas & Anne M. Mayes, 2008. "Science and technology for water purification in the coming decades," Nature, Nature, vol. 452(7185), pages 301-310, March.
    5. Mark Gersovitz & Jeffrey S. Hammer, 2003. "Infectious Diseases, Public Policy, and the Marriage of Economics and Epidemiology," The World Bank Research Observer, World Bank, vol. 18(2), pages 129-157.
    6. Brock, William & Xepapadeas, Anastasios, 2008. "Diffusion-induced instability and pattern formation in infinite horizon recursive optimal control," Journal of Economic Dynamics and Control, Elsevier, vol. 32(9), pages 2745-2787, September.
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    Cited by:

    1. Juliet Nakakawa & Joseph Y. T. Mugisha & Michael W. Shaw & William Tinzaara & Eldad Karamura, 2017. "Banana Xanthomonas Wilt Infection: The Role of Debudding and Roguing as Control Options within a Mixed Cultivar Plantation," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2017, pages 1-13, December.
    2. Jairos Kahuru & Livingstone S. Luboobi & Yaw Nkansah-Gyekye, 2017. "Optimal Control Techniques on a Mathematical Model for the Dynamics of Tungiasis in a Community," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2017, pages 1-19, August.
    3. Hellen Namawejje & Emmanuel Obuya & Livingstone S. Luboobi, 2018. "Modeling Optimal Control of Cholera Disease Under the Interventions of Vaccination, Treatment and Education Awareness," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 10(5), pages 137-152, October.

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