In this paper, a five compartmental model has been considered and investigated the transmission dynamics of measles disease in the human populations. The only one infected compartment in the standard model has been split into two: Infected catarrh, and infected eruption. Measles is a deadly disease that is very common and contagious in the world. However, if enough care is taken one can survive easily against Measles disease. The Measles disease has no specific treatment but vaccination is available. It has been shown that the model has a positive solution and is bounded. The basic reproduction number is derived using the next generation matrix method. The disease free equilibrium point is found and endemic equilibrium state is identified. It is shown that the disease free equilibrium point is locally and globally asymptotically stable if the reproduction number takes a value less than one unit and unstable if it is more than one unit. Numerical simulation study is conducted using ode 45 of MATLAB. The results and interpretations are elaborated and included in the text. Description of the model, Mathematical analysis, stability analysis, and simulation studies are conducted and the results are included. The standard model and the proposed models have been compared and the observations are presented in a tabular form.
| Published in | American Journal of Applied Mathematics (Volume 5, Issue 4) |
| DOI | 10.11648/j.ajam.20170504.11 |
| Page(s) | 99-107 |
| 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 |
Measles, Modeling, Equilibrium Points, Stability Analysis, Reproduction Number, Simulation Study
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APA Style
Selam Nigusie Mitku, Purnachandra Rao Koya. (2017). Mathematical Modeling and Simulation Study for the Control and Transmission Dynamics of Measles. American Journal of Applied Mathematics, 5(4), 99-107. https://doi.org/10.11648/j.ajam.20170504.11
ACS Style
Selam Nigusie Mitku; Purnachandra Rao Koya. Mathematical Modeling and Simulation Study for the Control and Transmission Dynamics of Measles. Am. J. Appl. Math. 2017, 5(4), 99-107. doi: 10.11648/j.ajam.20170504.11
AMA Style
Selam Nigusie Mitku, Purnachandra Rao Koya. Mathematical Modeling and Simulation Study for the Control and Transmission Dynamics of Measles. Am J Appl Math. 2017;5(4):99-107. doi: 10.11648/j.ajam.20170504.11
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Download@article{10.11648/j.ajam.20170504.11,
author = {Selam Nigusie Mitku and Purnachandra Rao Koya},
title = {Mathematical Modeling and Simulation Study for the Control and Transmission Dynamics of Measles},
journal = {American Journal of Applied Mathematics},
volume = {5},
number = {4},
pages = {99-107},
doi = {10.11648/j.ajam.20170504.11},
url = {https://doi.org/10.11648/j.ajam.20170504.11},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20170504.11},
abstract = {In this paper, a five compartmental model has been considered and investigated the transmission dynamics of measles disease in the human populations. The only one infected compartment in the standard model has been split into two: Infected catarrh, and infected eruption. Measles is a deadly disease that is very common and contagious in the world. However, if enough care is taken one can survive easily against Measles disease. The Measles disease has no specific treatment but vaccination is available. It has been shown that the model has a positive solution and is bounded. The basic reproduction number is derived using the next generation matrix method. The disease free equilibrium point is found and endemic equilibrium state is identified. It is shown that the disease free equilibrium point is locally and globally asymptotically stable if the reproduction number takes a value less than one unit and unstable if it is more than one unit. Numerical simulation study is conducted using ode 45 of MATLAB. The results and interpretations are elaborated and included in the text. Description of the model, Mathematical analysis, stability analysis, and simulation studies are conducted and the results are included. The standard model and the proposed models have been compared and the observations are presented in a tabular form.},
year = {2017}
}
TY - JOUR T1 - Mathematical Modeling and Simulation Study for the Control and Transmission Dynamics of Measles AU - Selam Nigusie Mitku AU - Purnachandra Rao Koya Y1 - 2017/07/06 PY - 2017 N1 - https://doi.org/10.11648/j.ajam.20170504.11 DO - 10.11648/j.ajam.20170504.11 T2 - American Journal of Applied Mathematics JF - American Journal of Applied Mathematics JO - American Journal of Applied Mathematics SP - 99 EP - 107 PB - Science Publishing Group SN - 2330-006X UR - https://doi.org/10.11648/j.ajam.20170504.11 AB - In this paper, a five compartmental model has been considered and investigated the transmission dynamics of measles disease in the human populations. The only one infected compartment in the standard model has been split into two: Infected catarrh, and infected eruption. Measles is a deadly disease that is very common and contagious in the world. However, if enough care is taken one can survive easily against Measles disease. The Measles disease has no specific treatment but vaccination is available. It has been shown that the model has a positive solution and is bounded. The basic reproduction number is derived using the next generation matrix method. The disease free equilibrium point is found and endemic equilibrium state is identified. It is shown that the disease free equilibrium point is locally and globally asymptotically stable if the reproduction number takes a value less than one unit and unstable if it is more than one unit. Numerical simulation study is conducted using ode 45 of MATLAB. The results and interpretations are elaborated and included in the text. Description of the model, Mathematical analysis, stability analysis, and simulation studies are conducted and the results are included. The standard model and the proposed models have been compared and the observations are presented in a tabular form. VL - 5 IS - 4 ER -
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