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

doi:10.1016/j.mcm.2010.11.060

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 journal › Article › peer-review

62 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 language	English
Pages (from-to)	1583-1595
Number of pages	13
Journal	Mathematical and Computer Modelling
Volume	53
Issue number	9-10
DOIs	https://doi.org/10.1016/j.mcm.2010.11.060
Publication status	Published - 1 May 2011
Externally published	Yes

Funding

The authors acknowledge with thanks the useful comments of the anonymous reviewers who contributed immensely to making this a better paper. SDHM acknowledges with thanks the support from the African Institute for Mathematical Sciences (AIMS) and the National University of Science and Technology (NUST). FN would like to thank the DST/NRF Centre of Excellence in Epidemiological Modelling and Analysis for its support in the production of this work. CC, PD, and ZM did this research at China Medical University and acknowledge with thanks financial support from the National Science Council of Taiwan .

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

SDG 2 Zero Hunger
SDG 3 Good Health and Well-being

Keywords

Cholera model
Equilibria
Malnutrition
Reproduction number
Stability
Susceptibility

ASJC Scopus subject areas

Modelling and Simulation
Computer Science Applications

Access to Document

10.1016/j.mcm.2010.11.060

Cite this

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title = "Modelling and analysis of the effects of malnutrition in the spread of cholera",

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.",

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AU - Hove-Musekwa, Senelani D.

AU - Nyabadza, Farai

AU - Chiyaka, Christinah

AU - Das, Prasenjit

AU - Tripathi, Agraj

AU - Mukandavire, Zindoga

PY - 2011/5/1

Y1 - 2011/5/1

N2 - 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.

AB - 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.

KW - Cholera model

KW - Equilibria

KW - Malnutrition

KW - Reproduction number

KW - Stability

KW - Susceptibility

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ER -

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

Abstract

Funding

UN SDGs

Keywords

ASJC Scopus subject areas

Access to Document

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Cite this