African Journal of
Mathematics and Computer Science Research

  • Abbreviation: Afr. J. Math. Comput. Sci. Res.
  • Language: English
  • ISSN: 2006-9731
  • DOI: 10.5897/AJMCSR
  • Start Year: 2008
  • Published Articles: 231

Full Length Research Paper

Optimal control model for the outbreak of cholera in Nigeria

Isere, A. O.
  • Isere, A. O.
  • Department of Mathematics and Statistics, Ambrose Alli University, Nigeria
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Osemwenkhae, J. E.
  • Osemwenkhae, J. E.
  • Department of Mathematics, University of Benin, Nigeria
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Okuonghae D.
  • Okuonghae D.
  • Department of Mathematics, University of Benin, Nigeria
  • Google Scholar


  •  Received: 20 January 2014
  •  Accepted: 01 April 2014
  •  Published: 30 April 2014

Abstract

In this work two mathematical models that described the dynamics of cholera in Nigeria were presented. The first model examined the bacteria population using a logistic definition for its growth in the expected habitat and their interaction with the susceptible population. The second model is an optimal control model that includes two time- dependent control functions with one minimizing the contact between the susceptible and the bacteria and the other, the population of the bacteria in the water. The results from the numerical solutions of the models presented showed that increasing the susceptible pool and the infected population above some threshold values were responsible for epidemic cholera. It also showed that the difference between the growth rate (r) and the loss rate (n) of the bacteria plays a huge role in the outbreak as well as the severity of the disease.

 

Key words: Cholera, mathematical model, optimal control model, numerical solutions.