A Mathematical Model for the Dynamics of Cholera with Control Measures

Stephen Edward; Nkuba Nyerere

doi:doi:10.11648/j.acm.20150402.14

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A Mathematical Model for the Dynamics of Cholera with Control Measures

Stephen Edward, Nkuba Nyerere

Published in Applied and Computational Mathematics (Volume 4, Issue 2)

Received: 25 February 2015 Accepted: 13 March 2015 Published: 21 March 2015

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Abstract

Cholera, an acute gastro-intestinal infection and a waterborne disease continues to emerge in developing countries and remains an important global health challenge. In this paper, we formulate a mathematical model that captures some essential dynamics of cholera transmission with public health educational campaigns, vaccination, sanitation and treatment as control strategies in limiting the disease. The reproduction numbers with single and combined controls are computed and compared with each other to assess the possible community benefits. Numerical simulation shows that in a unique control strategy, treatment yields the best results followed by education campaign, then sanitation and vaccination being the last. Furthermore, we noted that the control of cholera is very much better when we incorporated more than one strategy, in two controls the results were better than one strategy, and in three control strategies the results were far better than in two control strategies. Further simulations with all four interventions showed the best results among all combinations attained before. We performed sensitivity analysis on the key parameters that drive the disease dynamics in order to determine their relative importance to disease transmission and prevalence.

Published in	Applied and Computational Mathematics (Volume 4, Issue 2)
DOI	10.11648/j.acm.20150402.14
Page(s)	53-63
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

Modeling, Sensitivity, Sanitation, Education, Treatment, Vaccination, Epidemiology

References

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Stephen Edward, Nkuba Nyerere. (2015). A Mathematical Model for the Dynamics of Cholera with Control Measures. Applied and Computational Mathematics, 4(2), 53-63. https://doi.org/10.11648/j.acm.20150402.14

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Stephen Edward; Nkuba Nyerere. A Mathematical Model for the Dynamics of Cholera with Control Measures. Appl. Comput. Math. 2015, 4(2), 53-63. doi: 10.11648/j.acm.20150402.14

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Stephen Edward, Nkuba Nyerere. A Mathematical Model for the Dynamics of Cholera with Control Measures. Appl Comput Math. 2015;4(2):53-63. doi: 10.11648/j.acm.20150402.14

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@article{10.11648/j.acm.20150402.14,
  author = {Stephen Edward and Nkuba Nyerere},
  title = {A Mathematical Model for the Dynamics of Cholera with Control Measures},
  journal = {Applied and Computational Mathematics},
  volume = {4},
  number = {2},
  pages = {53-63},
  doi = {10.11648/j.acm.20150402.14},
  url = {https://doi.org/10.11648/j.acm.20150402.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20150402.14},
  abstract = {Cholera, an acute gastro-intestinal infection and a waterborne disease continues to emerge in developing countries and remains an important global health challenge. In this paper, we formulate a mathematical model that captures some essential dynamics of cholera transmission with public health educational campaigns, vaccination, sanitation and treatment as control strategies in limiting the disease. The reproduction numbers with single and combined controls are computed and compared with each other to assess the possible community benefits. Numerical simulation shows that in a unique control strategy, treatment yields the best results followed by education campaign, then sanitation and vaccination being the last. Furthermore, we noted that the control of cholera is very much better when we incorporated more than one strategy, in two controls the results were better than one strategy, and in three control strategies the results were far better than in two control strategies. Further simulations with all four interventions showed the best results among all combinations attained before. We performed sensitivity analysis on the key parameters that drive the disease dynamics in order to determine their relative importance to disease transmission and prevalence.},
 year = {2015}
}

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TY  - JOUR
T1  - A Mathematical Model for the Dynamics of Cholera with Control Measures
AU  - Stephen Edward
AU  - Nkuba Nyerere
Y1  - 2015/03/21
PY  - 2015
N1  - https://doi.org/10.11648/j.acm.20150402.14
DO  - 10.11648/j.acm.20150402.14
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 53
EP  - 63
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20150402.14
AB  - Cholera, an acute gastro-intestinal infection and a waterborne disease continues to emerge in developing countries and remains an important global health challenge. In this paper, we formulate a mathematical model that captures some essential dynamics of cholera transmission with public health educational campaigns, vaccination, sanitation and treatment as control strategies in limiting the disease. The reproduction numbers with single and combined controls are computed and compared with each other to assess the possible community benefits. Numerical simulation shows that in a unique control strategy, treatment yields the best results followed by education campaign, then sanitation and vaccination being the last. Furthermore, we noted that the control of cholera is very much better when we incorporated more than one strategy, in two controls the results were better than one strategy, and in three control strategies the results were far better than in two control strategies. Further simulations with all four interventions showed the best results among all combinations attained before. We performed sensitivity analysis on the key parameters that drive the disease dynamics in order to determine their relative importance to disease transmission and prevalence.
VL  - 4
IS  - 2
ER  -

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Author Information

Stephen Edward

Department of Mathematics, College of Natural and Mathematical Sciences, University of Dodoma, Dodoma, Tanzania
Nkuba Nyerere

Departments of Biometry and Mathematics, Sokoine University Of Agriculture, Morogoro, Tanzania

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Stephen Edward, Nkuba Nyerere. (2015). A Mathematical Model for the Dynamics of Cholera with Control Measures. Applied and Computational Mathematics, 4(2), 53-63. https://doi.org/10.11648/j.acm.20150402.14

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ACS Style

Stephen Edward; Nkuba Nyerere. A Mathematical Model for the Dynamics of Cholera with Control Measures. Appl. Comput. Math. 2015, 4(2), 53-63. doi: 10.11648/j.acm.20150402.14

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AMA Style

Stephen Edward, Nkuba Nyerere. A Mathematical Model for the Dynamics of Cholera with Control Measures. Appl Comput Math. 2015;4(2):53-63. doi: 10.11648/j.acm.20150402.14

Copy | Download

@article{10.11648/j.acm.20150402.14,
  author = {Stephen Edward and Nkuba Nyerere},
  title = {A Mathematical Model for the Dynamics of Cholera with Control Measures},
  journal = {Applied and Computational Mathematics},
  volume = {4},
  number = {2},
  pages = {53-63},
  doi = {10.11648/j.acm.20150402.14},
  url = {https://doi.org/10.11648/j.acm.20150402.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20150402.14},
  abstract = {Cholera, an acute gastro-intestinal infection and a waterborne disease continues to emerge in developing countries and remains an important global health challenge. In this paper, we formulate a mathematical model that captures some essential dynamics of cholera transmission with public health educational campaigns, vaccination, sanitation and treatment as control strategies in limiting the disease. The reproduction numbers with single and combined controls are computed and compared with each other to assess the possible community benefits. Numerical simulation shows that in a unique control strategy, treatment yields the best results followed by education campaign, then sanitation and vaccination being the last. Furthermore, we noted that the control of cholera is very much better when we incorporated more than one strategy, in two controls the results were better than one strategy, and in three control strategies the results were far better than in two control strategies. Further simulations with all four interventions showed the best results among all combinations attained before. We performed sensitivity analysis on the key parameters that drive the disease dynamics in order to determine their relative importance to disease transmission and prevalence.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - A Mathematical Model for the Dynamics of Cholera with Control Measures
AU  - Stephen Edward
AU  - Nkuba Nyerere
Y1  - 2015/03/21
PY  - 2015
N1  - https://doi.org/10.11648/j.acm.20150402.14
DO  - 10.11648/j.acm.20150402.14
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 53
EP  - 63
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20150402.14
AB  - Cholera, an acute gastro-intestinal infection and a waterborne disease continues to emerge in developing countries and remains an important global health challenge. In this paper, we formulate a mathematical model that captures some essential dynamics of cholera transmission with public health educational campaigns, vaccination, sanitation and treatment as control strategies in limiting the disease. The reproduction numbers with single and combined controls are computed and compared with each other to assess the possible community benefits. Numerical simulation shows that in a unique control strategy, treatment yields the best results followed by education campaign, then sanitation and vaccination being the last. Furthermore, we noted that the control of cholera is very much better when we incorporated more than one strategy, in two controls the results were better than one strategy, and in three control strategies the results were far better than in two control strategies. Further simulations with all four interventions showed the best results among all combinations attained before. We performed sensitivity analysis on the key parameters that drive the disease dynamics in order to determine their relative importance to disease transmission and prevalence.
VL  - 4
IS  - 2
ER  -

Copy | Download