In this paper, it is proposed and analyzed a new mathematical model and that is developed on the basis of some reasonable modification made to the standard epidemic model. The impact of immigration, treatment and the effect of vaccination are included in the model. The basic reproduction number is derived using the next generation matrix method. Disease free equilibrium point is found and endemic equilibrium state is identified. Numerical simulation study is conducted using ode 45 of MATLAB. It has been shown that the solution is positive and bounded. Algebraic expression for the reproduction number is constructed. Equilibrium points are identified and their stability analysis is carried out. It is pointed out that the disease dies out if the immigration of the infected dogs is controlled and the vaccination and the treatments are improved. Otherwise, the disease spreads rapidly in the dog population and it becomes an epidemic. Further, it is also pointed out that the impact of infective immigrants on the spread of dog rabies is positive and additive. The details are presented and discussed in the text.
| Published in | American Journal of Applied Mathematics (Volume 5, Issue 3) |
| DOI | 10.11648/j.ajam.20170503.12 |
| Page(s) | 68-77 |
| 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 |
Infective Immigrants, Rabies, Vaccination, Compartmental Model, Stability, Reproductive Number, Simulation
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APA Style
Aberu Mengistu Tulu, Purnachandra Rao Koya. (2017). The Impact of Infective Immigrants on the Spread of Dog Rabies. American Journal of Applied Mathematics, 5(3), 68-77. https://doi.org/10.11648/j.ajam.20170503.12
ACS Style
Aberu Mengistu Tulu; Purnachandra Rao Koya. The Impact of Infective Immigrants on the Spread of Dog Rabies. Am. J. Appl. Math. 2017, 5(3), 68-77. doi: 10.11648/j.ajam.20170503.12
AMA Style
Aberu Mengistu Tulu, Purnachandra Rao Koya. The Impact of Infective Immigrants on the Spread of Dog Rabies. Am J Appl Math. 2017;5(3):68-77. doi: 10.11648/j.ajam.20170503.12
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Download@article{10.11648/j.ajam.20170503.12,
author = {Aberu Mengistu Tulu and Purnachandra Rao Koya},
title = {The Impact of Infective Immigrants on the Spread of Dog Rabies},
journal = {American Journal of Applied Mathematics},
volume = {5},
number = {3},
pages = {68-77},
doi = {10.11648/j.ajam.20170503.12},
url = {https://doi.org/10.11648/j.ajam.20170503.12},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20170503.12},
abstract = {In this paper, it is proposed and analyzed a new mathematical model and that is developed on the basis of some reasonable modification made to the standard epidemic model. The impact of immigration, treatment and the effect of vaccination are included in the model. The basic reproduction number is derived using the next generation matrix method. Disease free equilibrium point is found and endemic equilibrium state is identified. Numerical simulation study is conducted using ode 45 of MATLAB. It has been shown that the solution is positive and bounded. Algebraic expression for the reproduction number is constructed. Equilibrium points are identified and their stability analysis is carried out. It is pointed out that the disease dies out if the immigration of the infected dogs is controlled and the vaccination and the treatments are improved. Otherwise, the disease spreads rapidly in the dog population and it becomes an epidemic. Further, it is also pointed out that the impact of infective immigrants on the spread of dog rabies is positive and additive. The details are presented and discussed in the text.},
year = {2017}
}
TY - JOUR T1 - The Impact of Infective Immigrants on the Spread of Dog Rabies AU - Aberu Mengistu Tulu AU - Purnachandra Rao Koya Y1 - 2017/06/23 PY - 2017 N1 - https://doi.org/10.11648/j.ajam.20170503.12 DO - 10.11648/j.ajam.20170503.12 T2 - American Journal of Applied Mathematics JF - American Journal of Applied Mathematics JO - American Journal of Applied Mathematics SP - 68 EP - 77 PB - Science Publishing Group SN - 2330-006X UR - https://doi.org/10.11648/j.ajam.20170503.12 AB - In this paper, it is proposed and analyzed a new mathematical model and that is developed on the basis of some reasonable modification made to the standard epidemic model. The impact of immigration, treatment and the effect of vaccination are included in the model. The basic reproduction number is derived using the next generation matrix method. Disease free equilibrium point is found and endemic equilibrium state is identified. Numerical simulation study is conducted using ode 45 of MATLAB. It has been shown that the solution is positive and bounded. Algebraic expression for the reproduction number is constructed. Equilibrium points are identified and their stability analysis is carried out. It is pointed out that the disease dies out if the immigration of the infected dogs is controlled and the vaccination and the treatments are improved. Otherwise, the disease spreads rapidly in the dog population and it becomes an epidemic. Further, it is also pointed out that the impact of infective immigrants on the spread of dog rabies is positive and additive. The details are presented and discussed in the text. VL - 5 IS - 3 ER -
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