Modelling Typhoid Fever with Education, Vaccination and Treatment

Stephen Edward; Nkuba Nyerere

doi:doi:10.11648/j.ijtam.20160202.30

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Modelling Typhoid Fever with Education, Vaccination and Treatment

Stephen Edward, Nkuba Nyerere

Published in International Journal of Theoretical and Applied Mathematics (Volume 2, Issue 2)

Received: 9 December 2016 Accepted: 27 December 2016 Published: 21 January 2017

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Abstract

Typhoid is among the most endemic diseases, and thus, of major public health concerns in tropical developing countries. In this study, we develop a deterministic compartmental mathematical model for assessing the effects of education campaigns, vaccination and treatment on controlling the transmission dynamics of typhoid fever in the community. We have shown that the disease free equilibrium state of the model is locally asymptotically stable if the basic reproduction number is less than unity. Careful analysis of the effective reproduction number has shown that, each of the intervention; education campaigns, vaccination or treatment has an effect in decreasing the transmission of typhoid fever in the community. Sensitivity analysis shows that, the most sensitive parameters are recovery rate for symptomatic infectious individuals, recruitment rate, vaccination rate, education campaign and transmission rate for carrier individuals. Both numerical and analytical results suggest that multiple control strategies are more effective than a single control strategy.

Published in	International Journal of Theoretical and Applied Mathematics (Volume 2, Issue 2)
DOI	10.11648/j.ijtam.20160202.30
Page(s)	156-164
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), 2017. Published by Science Publishing Group

Keywords

Typhoid, Reproductive Number, Treatment, Vaccination

References

[1]	Mushayabasa, S., Bhunu, CP., and Ngarakana-Gwasira ET. (2013) Mathematical analysis of a typhoid model with carriers, direct and indirect disease transmission. International Journal of Mathematical Sciences and Engineering Applications 7(I): 79-90.
[2]	Mushayabasa, S. (2012) A simple epidemiological model for typhoid with saturated incidence rate and treatment effect. World Academy of Science, Engineering and Technology, International Journal of Biological, Veterinary, Agricultural and Food Engineering 6(6): 56-63.
[3]	Pitzer, V. E., Cayley, C., Bowles, C. C., Baker, S., Kang, G., Balaji, V, Jeremy J. Farrar, J. J, Bryan, T., Grenfell, B. T. (2014) Predicting the Impact of Vaccination on the Transmission Dynamics of Typhoid in South Asia: A Mathematical Modeling Study. PLoS Neglected Tropical Diseases 8(1): e2642. doi: 10.1371/journal.pntd.0002642.
[4]	Buckle, G., Walker, C., Black, R. (2012) Typhoid fever and paratyphoid fever: Systematic review to estimate global morb-idity and mortality for 2010. J Glob Health 2: 1–9.
[5]	W. H. O. Background document: The diagnosis, treatment and prevention of typhoid fever, World Health Organization. 2003; 1-26.
[6]	Adetunde, I. A. (2008) A Mathematical models for the dynamics of typhoid fever in Kassena-Nankana district of upper east region of Ghana, J. Mod. Math. Stat. 2(2), 45-49.
[7]	Kalajdzievska, D. and LI, M. Y. (2011) Modeling the effects of carriers on transmission dynamics of infectious disease, Math. Biosci. Eng., 8(3), 711-722, http://dx.doi.org/10.39-34/mbe.2011.8.711.
[8]	Khan, M. A., Parvez, M., Islam, S., Khan, I., Shafie, S., and Gul, T. (2015) Mathematical Analysis of Typhoid Model with Saturated Incidence Rate, Advanced Studies in Biology, 7(2), 65–78.
[9]	Mushayabasa, S. (2014) Modeling the impact of optimal screening on typhoid dynamics, Int. J. Dynam. Control, Springer. DOI 10.1007/40435-014-0123-4.
[10]	O. Diekmann, J. A. P. Heesterbeek and M. G. Roberts. (2009) The construction of next generation matrices for compartmental epidemic models. J. R. Soc. Interface (doi:10.1098/rsif.2009.0386).
[11]	Van den Driessche, P and Watmough, J. (2002). Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Mathematical Biosciences. 180(1–2):29-48.
[12]	S. Mushayabasa. (2011) Impact of vaccines on Controlling typhoid fever in Kassena-Nankana District of upper east region of Ghana: insights from a mathematical model, Journal of Modern Mathematics and Statistics, vol. 5, no. 2, pp. 54–59.
[13]	D. T. Lauria, B. Maskery, C. Poulos, and D. Whittington. (2009)An optimization model for reducing typhoid cases in Developing countries without increasing public spending. Vaccine, vol. 27,no. 10, pp. 1609–1621.
[14]	Chitnis, N., Hyman, J. M., and Cusching, J. M. (2008). Determining important Parameters in the spread of malaria through the sensitivity analysis of a mathematical Model. Bulletin of Mathematical Biology 70 (5): 1272–12.

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Stephen Edward, Nkuba Nyerere. (2017). Modelling Typhoid Fever with Education, Vaccination and Treatment. International Journal of Theoretical and Applied Mathematics, 2(2), 156-164. https://doi.org/10.11648/j.ijtam.20160202.30

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ACS Style

Stephen Edward; Nkuba Nyerere. Modelling Typhoid Fever with Education, Vaccination and Treatment. Int. J. Theor. Appl. Math. 2017, 2(2), 156-164. doi: 10.11648/j.ijtam.20160202.30

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AMA Style

Stephen Edward, Nkuba Nyerere. Modelling Typhoid Fever with Education, Vaccination and Treatment. Int J Theor Appl Math. 2017;2(2):156-164. doi: 10.11648/j.ijtam.20160202.30

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@article{10.11648/j.ijtam.20160202.30,
  author = {Stephen Edward and Nkuba Nyerere},
  title = {Modelling Typhoid Fever with Education, Vaccination and Treatment},
  journal = {International Journal of Theoretical and Applied Mathematics},
  volume = {2},
  number = {2},
  pages = {156-164},
  doi = {10.11648/j.ijtam.20160202.30},
  url = {https://doi.org/10.11648/j.ijtam.20160202.30},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20160202.30},
  abstract = {Typhoid is among the most endemic diseases, and thus, of major public health concerns in tropical developing countries. In this study, we develop a deterministic compartmental mathematical model for assessing the effects of education campaigns, vaccination and treatment on controlling the transmission dynamics of typhoid fever in the community. We have shown that the disease free equilibrium state of the model is locally asymptotically stable if the basic reproduction number is less than unity. Careful analysis of the effective reproduction number has shown that, each of the intervention; education campaigns, vaccination or treatment has an effect in decreasing the transmission of typhoid fever in the community. Sensitivity analysis shows that, the most sensitive parameters are recovery rate for symptomatic infectious individuals, recruitment rate, vaccination rate, education campaign and transmission rate for carrier individuals. Both numerical and analytical results suggest that multiple control strategies are more effective than a single control strategy.},
 year = {2017}
}

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TY  - JOUR
T1  - Modelling Typhoid Fever with Education, Vaccination and Treatment
AU  - Stephen Edward
AU  - Nkuba Nyerere
Y1  - 2017/01/21
PY  - 2017
N1  - https://doi.org/10.11648/j.ijtam.20160202.30
DO  - 10.11648/j.ijtam.20160202.30
T2  - International Journal of Theoretical and Applied Mathematics
JF  - International Journal of Theoretical and Applied Mathematics
JO  - International Journal of Theoretical and Applied Mathematics
SP  - 156
EP  - 164
PB  - Science Publishing Group
SN  - 2575-5080
UR  - https://doi.org/10.11648/j.ijtam.20160202.30
AB  - Typhoid is among the most endemic diseases, and thus, of major public health concerns in tropical developing countries. In this study, we develop a deterministic compartmental mathematical model for assessing the effects of education campaigns, vaccination and treatment on controlling the transmission dynamics of typhoid fever in the community. We have shown that the disease free equilibrium state of the model is locally asymptotically stable if the basic reproduction number is less than unity. Careful analysis of the effective reproduction number has shown that, each of the intervention; education campaigns, vaccination or treatment has an effect in decreasing the transmission of typhoid fever in the community. Sensitivity analysis shows that, the most sensitive parameters are recovery rate for symptomatic infectious individuals, recruitment rate, vaccination rate, education campaign and transmission rate for carrier individuals. Both numerical and analytical results suggest that multiple control strategies are more effective than a single control strategy.
VL  - 2
IS  - 2
ER  -

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Author Information

Stephen Edward

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

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

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APA Style

Stephen Edward, Nkuba Nyerere. (2017). Modelling Typhoid Fever with Education, Vaccination and Treatment. International Journal of Theoretical and Applied Mathematics, 2(2), 156-164. https://doi.org/10.11648/j.ijtam.20160202.30

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ACS Style

Stephen Edward; Nkuba Nyerere. Modelling Typhoid Fever with Education, Vaccination and Treatment. Int. J. Theor. Appl. Math. 2017, 2(2), 156-164. doi: 10.11648/j.ijtam.20160202.30

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AMA Style

Stephen Edward, Nkuba Nyerere. Modelling Typhoid Fever with Education, Vaccination and Treatment. Int J Theor Appl Math. 2017;2(2):156-164. doi: 10.11648/j.ijtam.20160202.30

Copy | Download

@article{10.11648/j.ijtam.20160202.30,
  author = {Stephen Edward and Nkuba Nyerere},
  title = {Modelling Typhoid Fever with Education, Vaccination and Treatment},
  journal = {International Journal of Theoretical and Applied Mathematics},
  volume = {2},
  number = {2},
  pages = {156-164},
  doi = {10.11648/j.ijtam.20160202.30},
  url = {https://doi.org/10.11648/j.ijtam.20160202.30},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20160202.30},
  abstract = {Typhoid is among the most endemic diseases, and thus, of major public health concerns in tropical developing countries. In this study, we develop a deterministic compartmental mathematical model for assessing the effects of education campaigns, vaccination and treatment on controlling the transmission dynamics of typhoid fever in the community. We have shown that the disease free equilibrium state of the model is locally asymptotically stable if the basic reproduction number is less than unity. Careful analysis of the effective reproduction number has shown that, each of the intervention; education campaigns, vaccination or treatment has an effect in decreasing the transmission of typhoid fever in the community. Sensitivity analysis shows that, the most sensitive parameters are recovery rate for symptomatic infectious individuals, recruitment rate, vaccination rate, education campaign and transmission rate for carrier individuals. Both numerical and analytical results suggest that multiple control strategies are more effective than a single control strategy.},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - Modelling Typhoid Fever with Education, Vaccination and Treatment
AU  - Stephen Edward
AU  - Nkuba Nyerere
Y1  - 2017/01/21
PY  - 2017
N1  - https://doi.org/10.11648/j.ijtam.20160202.30
DO  - 10.11648/j.ijtam.20160202.30
T2  - International Journal of Theoretical and Applied Mathematics
JF  - International Journal of Theoretical and Applied Mathematics
JO  - International Journal of Theoretical and Applied Mathematics
SP  - 156
EP  - 164
PB  - Science Publishing Group
SN  - 2575-5080
UR  - https://doi.org/10.11648/j.ijtam.20160202.30
AB  - Typhoid is among the most endemic diseases, and thus, of major public health concerns in tropical developing countries. In this study, we develop a deterministic compartmental mathematical model for assessing the effects of education campaigns, vaccination and treatment on controlling the transmission dynamics of typhoid fever in the community. We have shown that the disease free equilibrium state of the model is locally asymptotically stable if the basic reproduction number is less than unity. Careful analysis of the effective reproduction number has shown that, each of the intervention; education campaigns, vaccination or treatment has an effect in decreasing the transmission of typhoid fever in the community. Sensitivity analysis shows that, the most sensitive parameters are recovery rate for symptomatic infectious individuals, recruitment rate, vaccination rate, education campaign and transmission rate for carrier individuals. Both numerical and analytical results suggest that multiple control strategies are more effective than a single control strategy.
VL  - 2
IS  - 2
ER  -

Copy | Download