Modelling and Analysis of the Intrinsic Dynamics of Cholera

Z. Mukandavire, A. Tripathi, C. Chiyaka, G. Musuka, F. Nyabadza, H. G. Mwambi

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16 Citations (Scopus)

Abstract

A simple mathematical model for cholera is presented using a system of ordinary differential equations. Comprehensive analysis of the important mathematical features of the model is carried out. The disease-free and endemic equilibria are obtained and their local stability investigated. We use the centre manifold theory to show the stability of the endemic equilibrium and suitable Lyapunov function for its global stability. Qualitative analysis of the model including positivity and boundedness of solutions are also presented. The cholera model is numerically analysed using published data to explore the effects of the recovery rate, rate of exposure to contaminated water and contribution of infected individuals to the population of Vibrio cholerae in the aquatic environment on the cumulative number of cholera infected individuals. The results demonstrate that proper management of the diseases will reduce the burden of cholera in endemic areas.

Original languageEnglish
Pages (from-to)253-265
Number of pages13
JournalDifferential Equations and Dynamical Systems
Volume19
Issue number3
Early online date22 Apr 2011
DOIs
Publication statusPublished - 1 Jul 2011
Externally publishedYes

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Keywords

  • Cholera model
  • Equilibria
  • Reproduction number
  • Stability

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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