Mathematical Modelling of Epidemiology of Malaria: A Case Study of Luapula Province of Zambia

Justina Mulenga; Leonard Mubila

doi:doi:10.11648/j.ajam.20160406.15

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Mathematical Modelling of Epidemiology of Malaria: A Case Study of Luapula Province of Zambia

Justina Mulenga, Leonard Mubila

Published in American Journal of Applied Mathematics (Volume 4, Issue 6)

Received: 10 March 2016 Accepted: 18 March 2016 Published: 25 November 2016

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Abstract

In this study, we use the SIR model proposed by Kermack and McKendrick to model the epidemiology of malaria in Luapula Province. Data collected from the District Health Management Teams in Luapula Province were used to analyse the rate of infection of malaria in the Province. The Reproduction number R₀, was calculated and it was found if R₀ >0, there will be malaria outbreak in the province and if R₀<0, the disease will not evade the Province. From our analysis we found R₀ >0 which implies that the force of malaria infection in the Province is high. We, therefore, make recommendations for the reduction of malaria in the Province.

Published in	American Journal of Applied Mathematics (Volume 4, Issue 6)
DOI	10.11648/j.ajam.20160406.15
Page(s)	289-295
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

SIR, Reproduction Number, Malaria, Luapula Province

References

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[3]	Chitnis, N., Cushing J.M., and Hyman, M (2008) Determining important parameters in the spread of malaria through the sensitivity analysis of a mathematical model. Bulletin of Mathematical Biology, 70:12721296.
[4]	Central Statistical Office (CSO), Ministry of Health (MOH), Tropical Diseases Research Centre.
[5]	(TDRC), University of Zambia (UNZA) and ORC Macro. (2009). Zambia Demographic and Health Survey 2007: Calverton, Maryland, USA: Central Statistical Office, Central Board of Health, and ORC Macro.
[6]	Hove-Musekwa, S. D. (2008). Determining effective spraying periods to control malaria via indoor residual spraying in sub-saharan Africa. Advances in Decision Sciences, 2008.
[7]	Johansson P. Leander J., (2010) Mathematical Modeling of Malaria - Methods for Simulation of Epidemics, Chalmers University of Technology, Gothenburg.
[8]	King, A. T., Mends–Brew, E., Osei–Frimpong, E., &Ohene, K. R. (2012). Mathematical model for the control of malaria–Case study: Chorkor polyclinic, Accra, Ghana.
[9]	Lalloo, D. G., Shingadia, D., Pasvol, G., Chiodini, P. L., Whitty, C. J., Beeching, N. J., ... & Bannister, B. A. (2007). UK malaria treatment guidelines. Journal of infection, 54(2), 111-121.
[10]	MacDonald. G, (1957) The Epidemiology and Control of Malaria. Oxford University Press, London.
[11]	Mandal, S., Sarkar, R. R., & Sinha, S. (2011). Mathematical models of malaria-a review. Malar J, 10, 202.
[12]	Ministry of Health (MOH) [Zambia]. 2008c. National Malaria Control Action Plan 2008. Lusaka,Zambia: Ministry of Health
[13]	Ngwa, G. A., &Shu, W. S. (2000). A mathematical model for endemic malaria with variable human and mosquito populations. Mathematical and computer modelling, 32(7), 747-763.
[14]	Tumwiine, J., Mugisha, J. Y. T., &Luboobi, L. S. (2007). A mathematical model for the dynamics of malaria in a human host and mosquito vector with temporary immunity. Applied mathematics and computation, 189(2), 1953-1965.
[15]	World Health Organization (2012), World Malaria Report 2012FACT SHEETwww.who.int/malaria/publications/world_report_2012/wmr 2012, retrieved on Wednesday 27th November, 2013.

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Justina Mulenga, Leonard Mubila. (2016). Mathematical Modelling of Epidemiology of Malaria: A Case Study of Luapula Province of Zambia. American Journal of Applied Mathematics, 4(6), 289-295. https://doi.org/10.11648/j.ajam.20160406.15

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ACS Style

Justina Mulenga; Leonard Mubila. Mathematical Modelling of Epidemiology of Malaria: A Case Study of Luapula Province of Zambia. Am. J. Appl. Math. 2016, 4(6), 289-295. doi: 10.11648/j.ajam.20160406.15

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AMA Style

Justina Mulenga, Leonard Mubila. Mathematical Modelling of Epidemiology of Malaria: A Case Study of Luapula Province of Zambia. Am J Appl Math. 2016;4(6):289-295. doi: 10.11648/j.ajam.20160406.15

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@article{10.11648/j.ajam.20160406.15,
  author = {Justina Mulenga and Leonard Mubila},
  title = {Mathematical Modelling of Epidemiology of Malaria: A Case Study of Luapula Province of Zambia},
  journal = {American Journal of Applied Mathematics},
  volume = {4},
  number = {6},
  pages = {289-295},
  doi = {10.11648/j.ajam.20160406.15},
  url = {https://doi.org/10.11648/j.ajam.20160406.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20160406.15},
  abstract = {In this study, we use the SIR model proposed by Kermack and McKendrick to model the epidemiology of malaria in Luapula Province. Data collected from the District Health Management Teams in Luapula Province were used to analyse the rate of infection of malaria in the Province. The Reproduction number R0, was calculated and it was found if R0 >0, there will be malaria outbreak in the province and if R0<0, the disease will not evade the Province. From our analysis we found R0 >0 which implies that the force of malaria infection in the Province is high. We, therefore, make recommendations for the reduction of malaria in the Province.},
 year = {2016}
}

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TY  - JOUR
T1  - Mathematical Modelling of Epidemiology of Malaria: A Case Study of Luapula Province of Zambia
AU  - Justina Mulenga
AU  - Leonard Mubila
Y1  - 2016/11/25
PY  - 2016
N1  - https://doi.org/10.11648/j.ajam.20160406.15
DO  - 10.11648/j.ajam.20160406.15
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
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PB  - Science Publishing Group
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AB  - In this study, we use the SIR model proposed by Kermack and McKendrick to model the epidemiology of malaria in Luapula Province. Data collected from the District Health Management Teams in Luapula Province were used to analyse the rate of infection of malaria in the Province. The Reproduction number R0, was calculated and it was found if R0 >0, there will be malaria outbreak in the province and if R0<0, the disease will not evade the Province. From our analysis we found R0 >0 which implies that the force of malaria infection in the Province is high. We, therefore, make recommendations for the reduction of malaria in the Province.
VL  - 4
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Author Information

Justina Mulenga

Department of Mathematics, School of Mathematics and Natural Sciences, The Copperbelt University, Kitwe, Zambia
Leonard Mubila

Department of Mathematics, School of Mathematics and Natural Sciences, The Copperbelt University, Kitwe, Zambia

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APA Style

Justina Mulenga, Leonard Mubila. (2016). Mathematical Modelling of Epidemiology of Malaria: A Case Study of Luapula Province of Zambia. American Journal of Applied Mathematics, 4(6), 289-295. https://doi.org/10.11648/j.ajam.20160406.15

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ACS Style

Justina Mulenga; Leonard Mubila. Mathematical Modelling of Epidemiology of Malaria: A Case Study of Luapula Province of Zambia. Am. J. Appl. Math. 2016, 4(6), 289-295. doi: 10.11648/j.ajam.20160406.15

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AMA Style

Justina Mulenga, Leonard Mubila. Mathematical Modelling of Epidemiology of Malaria: A Case Study of Luapula Province of Zambia. Am J Appl Math. 2016;4(6):289-295. doi: 10.11648/j.ajam.20160406.15

Copy | Download

@article{10.11648/j.ajam.20160406.15,
  author = {Justina Mulenga and Leonard Mubila},
  title = {Mathematical Modelling of Epidemiology of Malaria: A Case Study of Luapula Province of Zambia},
  journal = {American Journal of Applied Mathematics},
  volume = {4},
  number = {6},
  pages = {289-295},
  doi = {10.11648/j.ajam.20160406.15},
  url = {https://doi.org/10.11648/j.ajam.20160406.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20160406.15},
  abstract = {In this study, we use the SIR model proposed by Kermack and McKendrick to model the epidemiology of malaria in Luapula Province. Data collected from the District Health Management Teams in Luapula Province were used to analyse the rate of infection of malaria in the Province. The Reproduction number R0, was calculated and it was found if R0 >0, there will be malaria outbreak in the province and if R0<0, the disease will not evade the Province. From our analysis we found R0 >0 which implies that the force of malaria infection in the Province is high. We, therefore, make recommendations for the reduction of malaria in the Province.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - Mathematical Modelling of Epidemiology of Malaria: A Case Study of Luapula Province of Zambia
AU  - Justina Mulenga
AU  - Leonard Mubila
Y1  - 2016/11/25
PY  - 2016
N1  - https://doi.org/10.11648/j.ajam.20160406.15
DO  - 10.11648/j.ajam.20160406.15
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 289
EP  - 295
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20160406.15
AB  - In this study, we use the SIR model proposed by Kermack and McKendrick to model the epidemiology of malaria in Luapula Province. Data collected from the District Health Management Teams in Luapula Province were used to analyse the rate of infection of malaria in the Province. The Reproduction number R0, was calculated and it was found if R0 >0, there will be malaria outbreak in the province and if R0<0, the disease will not evade the Province. From our analysis we found R0 >0 which implies that the force of malaria infection in the Province is high. We, therefore, make recommendations for the reduction of malaria in the Province.
VL  - 4
IS  - 6
ER  -

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