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Modeling Optimal Control of Cholera Disease Under the Interventions of Vaccination, Treatment and Education Awareness

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  • Hellen Namawejje
  • Emmanuel Obuya
  • Livingstone S. Luboobi

Abstract

Cholera is virulent disease that affects both children and adults and can kill within hours. It has long been, and continues to be, a global threat to public health regardless of the advancement of medical science and health care service available. In this paper we formulate and analyze a mathematical model of the dynamics and optimal con- trol strategies for cholera epidemic. We present and analyze a cholera model with controls: u1 for vaccination of the human population, u2 for treatment and u3 for health education campaigns. The basic reproductive number R0; the effective reproductive number Re; as well as disease free equilibrium and endemic equilibrium points are derived. We establish the conditions for optimal control of the cholera disease using the Pontryagin's maximum principle and simulate the model for different control strategies. The results show that vaccination and education campaigns should be applied from start of the epidemic in any community faced with cholera disease.

Suggested Citation

  • 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.
    • Handle: RePEc:ibn:jmrjnl:v:10:y:2018:i:5:p:137
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    References listed on IDEAS

    as
    1. 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.
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    More about this item

    Keywords

    cholera epidemic; optimal control; Pontryagin's maximum principle; Basic and effective reproductive numbers;
    All these keywords.

    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

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