Modelling and analysis of the effects of malnutrition in the spread of cholera

Senelani D. Hove-Musekwa, Farai Nyabadza, Christinah Chiyaka, Prasenjit Das, Agraj Tripathi, Zindoga Mukandavire

Research output: Contribution to journalArticle

23 Citations (Scopus)

Abstract

Although cholera has existed for ages, it has continued to plague many parts of the world. In this study, a deterministic model for cholera in a community is presented and rigorously analysed in order to determine the effects of malnutrition in the spread of the disease. The important mathematical features of the cholera model are thoroughly investigated. The epidemic threshold known as the basic reproductive number and equilibria for the model are determined, and stabilities are investigated. The disease-free equilibrium is shown to be globally asymptotically stable. Local stability of the endemic equilibrium is determined using centre manifold theory and conditions for its global stability are derived using a suitable Lyapunov function. Numerical simulations suggest that an increase in susceptibility to cholera due to malnutrition results in an increase in the number of cholera infected individuals in a community. The results suggest that nutritional issues should be addressed in impoverished communities affected by cholera in order to reduce the burden of the disease.

Original languageEnglish
Pages (from-to)1583-1595
Number of pages13
JournalMathematical and Computer Modelling
Volume53
Issue number9-10
DOIs
Publication statusPublished - 1 May 2011
Externally publishedYes

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Modeling
Basic Reproductive number
Endemic Equilibrium
Center Manifold
Globally Asymptotically Stable
Local Stability
Deterministic Model
Lyapunov functions
Global Stability
Lyapunov Function
Susceptibility
Numerical Simulation
Computer simulation
Model
Community

Keywords

  • Cholera model
  • Equilibria
  • Malnutrition
  • Reproduction number
  • Stability
  • Susceptibility

ASJC Scopus subject areas

  • Modelling and Simulation
  • Computer Science Applications

Cite this

Modelling and analysis of the effects of malnutrition in the spread of cholera. / Hove-Musekwa, Senelani D.; Nyabadza, Farai; Chiyaka, Christinah; Das, Prasenjit; Tripathi, Agraj; Mukandavire, Zindoga.

In: Mathematical and Computer Modelling, Vol. 53, No. 9-10, 01.05.2011, p. 1583-1595.

Research output: Contribution to journalArticle

Hove-Musekwa, Senelani D. ; Nyabadza, Farai ; Chiyaka, Christinah ; Das, Prasenjit ; Tripathi, Agraj ; Mukandavire, Zindoga. / Modelling and analysis of the effects of malnutrition in the spread of cholera. In: Mathematical and Computer Modelling. 2011 ; Vol. 53, No. 9-10. pp. 1583-1595.
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