Modeling the Dynamics of Rabies Transmission with Vaccination and Stability Analysis

Tesfaye Tadesse Ega; Livingstone S. Luboobi; Dmitry Kuznetsov

doi:doi:10.11648/j.acm.20150406.13

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Modeling the Dynamics of Rabies Transmission with Vaccination and Stability Analysis

Tesfaye Tadesse Ega, Livingstone S. Luboobi, Dmitry Kuznetsov

Published in Applied and Computational Mathematics (Volume 4, Issue 6)

Received: 7 September 2015 Accepted: 21 September 2015 Published: 10 October 2015

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Abstract

In this paper we formulate a deterministic mathematical model for the transmission dynamics of rabies in human and animal within and around Addis Ababa, Ethiopia. Our model involves vaccination program for dog population. The basic reproduction number and effective reproduction numbers are computed and the results are entirely depending on the parameters of dog population, which shows the responsibility of dog population for human and livestock infection. For a specified set of values of parameters as deduced from the data provided by Ethiopian Public Health Institute of Addis Ababa, the basic reproduction number R₀ and the effective reproduction number R_e works out to be 2 and 1.6 respectively, which indicates the disease will be endemic. The numerical simulation of reproduction ratio shows that the combination of vaccination, culling of stray dogs and controlling annual crop of new born puppies are the best method to control rabies transmission within and around Adds Ababa. The disease - free equilibrium ε₀ is computed. When the effective reproduction number R_e<1 it is proved to be globally asymptotically stable in the feasible region Φ. When R_e>1 there exists one endemic equilibrium point which is locally asymptotically stable.

Published in	Applied and Computational Mathematics (Volume 4, Issue 6)
DOI	10.11648/j.acm.20150406.13
Page(s)	409-419
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), 2015. Published by Science Publishing Group

Keywords

Rabies, Addis Ababa, Endemic, Reproduction Number, Equilibrium Points

References

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[6]	A. Deressa, A. Ali, M. Bayene, N. Selassie, E. Yimer and K. Hussen, The status of rabies in Ethiopia: A retrospective record review, Ethiopian Journal of Health Development. 24 (2010), 1 - 6.
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[10]	W. T. Jemberu, W. Molla, G. Almaw and S. Alemu, Incidence of rabies in humans anddomestic animals and people's awareness in North Gondar Zone, Ethiopia, PLoS Negl. Trop. Dis. 7 (2013).
[11]	S. Khan, Rabies molecular virology, diagnosis, prevention and treatment, 2012. Available oline at http: //www. biomedcentral. com/ content/ pdf/1743 - 422X - 9 - 50. pdf. Retrieved 13 April 2015.
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APA Style

Tesfaye Tadesse Ega, Livingstone S. Luboobi, Dmitry Kuznetsov. (2015). Modeling the Dynamics of Rabies Transmission with Vaccination and Stability Analysis. Applied and Computational Mathematics, 4(6), 409-419. https://doi.org/10.11648/j.acm.20150406.13

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ACS Style

Tesfaye Tadesse Ega; Livingstone S. Luboobi; Dmitry Kuznetsov. Modeling the Dynamics of Rabies Transmission with Vaccination and Stability Analysis. Appl. Comput. Math. 2015, 4(6), 409-419. doi: 10.11648/j.acm.20150406.13

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AMA Style

Tesfaye Tadesse Ega, Livingstone S. Luboobi, Dmitry Kuznetsov. Modeling the Dynamics of Rabies Transmission with Vaccination and Stability Analysis. Appl Comput Math. 2015;4(6):409-419. doi: 10.11648/j.acm.20150406.13

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@article{10.11648/j.acm.20150406.13,
  author = {Tesfaye Tadesse Ega and Livingstone S. Luboobi and Dmitry Kuznetsov},
  title = {Modeling the Dynamics of Rabies Transmission with Vaccination and Stability Analysis},
  journal = {Applied and Computational Mathematics},
  volume = {4},
  number = {6},
  pages = {409-419},
  doi = {10.11648/j.acm.20150406.13},
  url = {https://doi.org/10.11648/j.acm.20150406.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20150406.13},
  abstract = {In this paper we formulate a deterministic mathematical model for the transmission dynamics of rabies in human and animal within and around Addis Ababa, Ethiopia. Our model involves vaccination program for dog population. The   basic reproduction number and effective reproduction numbers are computed and the results are entirely depending on the parameters of dog population, which shows the responsibility of dog population for human and livestock   infection. For a specified set of values of parameters as deduced from the data provided by Ethiopian Public Health Institute of Addis Ababa, the basic reproduction number R0 and the effective reproduction number   Re works out to be 2 and 1.6 respectively, which indicates the disease will be endemic. The numerical simulation of reproduction ratio shows that the combination of vaccination, culling of stray dogs and controlling   annual crop of new born puppies are the best method to control rabies transmission within and around Adds Ababa. The disease - free equilibrium ε0 is computed. When the effective reproduction number   Re<1 it is proved to be globally asymptotically stable in the feasible region Φ. When Re>1 there exists one endemic equilibrium point which is locally asymptotically stable.},
 year = {2015}
}

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TY  - JOUR
T1  - Modeling the Dynamics of Rabies Transmission with Vaccination and Stability Analysis
AU  - Tesfaye Tadesse Ega
AU  - Livingstone S. Luboobi
AU  - Dmitry Kuznetsov
Y1  - 2015/10/10
PY  - 2015
N1  - https://doi.org/10.11648/j.acm.20150406.13
DO  - 10.11648/j.acm.20150406.13
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 409
EP  - 419
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20150406.13
AB  - In this paper we formulate a deterministic mathematical model for the transmission dynamics of rabies in human and animal within and around Addis Ababa, Ethiopia. Our model involves vaccination program for dog population. The   basic reproduction number and effective reproduction numbers are computed and the results are entirely depending on the parameters of dog population, which shows the responsibility of dog population for human and livestock   infection. For a specified set of values of parameters as deduced from the data provided by Ethiopian Public Health Institute of Addis Ababa, the basic reproduction number R0 and the effective reproduction number   Re works out to be 2 and 1.6 respectively, which indicates the disease will be endemic. The numerical simulation of reproduction ratio shows that the combination of vaccination, culling of stray dogs and controlling   annual crop of new born puppies are the best method to control rabies transmission within and around Adds Ababa. The disease - free equilibrium ε0 is computed. When the effective reproduction number   Re<1 it is proved to be globally asymptotically stable in the feasible region Φ. When Re>1 there exists one endemic equilibrium point which is locally asymptotically stable.
VL  - 4
IS  - 6
ER  -

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Author Information

Tesfaye Tadesse Ega

CoCSE School, Nelson Mandela African Institution of Science and Technology, Arusha, Tanzania
Livingstone S. Luboobi

CoCSE School, Nelson Mandela African Institution of Science and Technology, Arusha, Tanzania
Dmitry Kuznetsov

CoCSE School, Nelson Mandela African Institution of Science and Technology, Arusha, Tanzania

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APA Style

Tesfaye Tadesse Ega, Livingstone S. Luboobi, Dmitry Kuznetsov. (2015). Modeling the Dynamics of Rabies Transmission with Vaccination and Stability Analysis. Applied and Computational Mathematics, 4(6), 409-419. https://doi.org/10.11648/j.acm.20150406.13

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ACS Style

Tesfaye Tadesse Ega; Livingstone S. Luboobi; Dmitry Kuznetsov. Modeling the Dynamics of Rabies Transmission with Vaccination and Stability Analysis. Appl. Comput. Math. 2015, 4(6), 409-419. doi: 10.11648/j.acm.20150406.13

Copy | Download

AMA Style

Tesfaye Tadesse Ega, Livingstone S. Luboobi, Dmitry Kuznetsov. Modeling the Dynamics of Rabies Transmission with Vaccination and Stability Analysis. Appl Comput Math. 2015;4(6):409-419. doi: 10.11648/j.acm.20150406.13

Copy | Download

@article{10.11648/j.acm.20150406.13,
  author = {Tesfaye Tadesse Ega and Livingstone S. Luboobi and Dmitry Kuznetsov},
  title = {Modeling the Dynamics of Rabies Transmission with Vaccination and Stability Analysis},
  journal = {Applied and Computational Mathematics},
  volume = {4},
  number = {6},
  pages = {409-419},
  doi = {10.11648/j.acm.20150406.13},
  url = {https://doi.org/10.11648/j.acm.20150406.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20150406.13},
  abstract = {In this paper we formulate a deterministic mathematical model for the transmission dynamics of rabies in human and animal within and around Addis Ababa, Ethiopia. Our model involves vaccination program for dog population. The   basic reproduction number and effective reproduction numbers are computed and the results are entirely depending on the parameters of dog population, which shows the responsibility of dog population for human and livestock   infection. For a specified set of values of parameters as deduced from the data provided by Ethiopian Public Health Institute of Addis Ababa, the basic reproduction number R0 and the effective reproduction number   Re works out to be 2 and 1.6 respectively, which indicates the disease will be endemic. The numerical simulation of reproduction ratio shows that the combination of vaccination, culling of stray dogs and controlling   annual crop of new born puppies are the best method to control rabies transmission within and around Adds Ababa. The disease - free equilibrium ε0 is computed. When the effective reproduction number   Re<1 it is proved to be globally asymptotically stable in the feasible region Φ. When Re>1 there exists one endemic equilibrium point which is locally asymptotically stable.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - Modeling the Dynamics of Rabies Transmission with Vaccination and Stability Analysis
AU  - Tesfaye Tadesse Ega
AU  - Livingstone S. Luboobi
AU  - Dmitry Kuznetsov
Y1  - 2015/10/10
PY  - 2015
N1  - https://doi.org/10.11648/j.acm.20150406.13
DO  - 10.11648/j.acm.20150406.13
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 409
EP  - 419
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20150406.13
AB  - In this paper we formulate a deterministic mathematical model for the transmission dynamics of rabies in human and animal within and around Addis Ababa, Ethiopia. Our model involves vaccination program for dog population. The   basic reproduction number and effective reproduction numbers are computed and the results are entirely depending on the parameters of dog population, which shows the responsibility of dog population for human and livestock   infection. For a specified set of values of parameters as deduced from the data provided by Ethiopian Public Health Institute of Addis Ababa, the basic reproduction number R0 and the effective reproduction number   Re works out to be 2 and 1.6 respectively, which indicates the disease will be endemic. The numerical simulation of reproduction ratio shows that the combination of vaccination, culling of stray dogs and controlling   annual crop of new born puppies are the best method to control rabies transmission within and around Adds Ababa. The disease - free equilibrium ε0 is computed. When the effective reproduction number   Re<1 it is proved to be globally asymptotically stable in the feasible region Φ. When Re>1 there exists one endemic equilibrium point which is locally asymptotically stable.
VL  - 4
IS  - 6
ER  -

Copy | Download