Modeling and Analysis of Malt-Drug Resistance Tuberculosis in Densly Populated Areas

Dancho Desaleng; Purnachandra Rao Koya

doi:doi:10.11648/j.ajam.20160401.11

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Modeling and Analysis of Malt-Drug Resistance Tuberculosis in Densly Populated Areas

Dancho Desaleng, Purnachandra Rao Koya

Published in American Journal of Applied Mathematics (Volume 4, Issue 1)

Received: 18 November 2015 Accepted: 4 December 2015 Published: 4 January 2016

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Abstract

Tuberculosis is an airborne disease caused by the bacterium called mycobacterium tuberculosis. We have compartmentalized the population based on the exposed level to the disease and described the flow using a flowchart. Mathematical model is developed to describe the population dynamics of the compartments. The migration of people from infected class to exposed class, due to failure of continuing the medicine for any reason, is called here as Malt – drug resistance tuberculosis. The equilibrium points identified are disease free, endemic and epidemic. Equilibrium point analysis is made and has been included. Formula for reproduction number is derived. Numerical simulation study of the Mathematical model is conducted using ode45 function of MATLAB software. It is shown that the propagation of the disease is more in the more populated areas and less in the less populated areas.

Published in	American Journal of Applied Mathematics (Volume 4, Issue 1)
DOI	10.11648/j.ajam.20160401.11
Page(s)	1-10
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), 2016. Published by Science Publishing Group

Keywords

Tuberculosis, Mathematical Modeling, Equilibrium Points, Basic Reproduction Number, Stability Analysis, Numerical Simulation

References

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[2]	Dr. Maria Sanchez, Lecture 9: Tuberculosis pdf UC Berkeley Ongoing TB and HIV research.
[3]	Hongbin Guo and Michael Y. Li. Global stability in a Mathematical Model of Tuberculosis. Canadian Applied Mathematics Quarterly, Volume 14, Number 2, Summer 2006.
[4]	PHAC. "Tuberculosis FACT SHEETS." 2008. http://www.phac-aspc.gc.ca/tbpclatb/fa-fi/trans-eng.php.
[5]	Global Tuberculosis Report 2012. World Health Organization 20 Avenue Appia, 1211-Geneva-27, Switzerland Email: tbdocs@who.int Web site: www.who.int/tb.
[6]	Global tuberculosis report 2013. World Health Organization. Geneva: 23 Oct 2013. Available from: http://apps.who.int/iris/bitstream/10665/91355/1/9789241564656-eng.pdf.
[7]	World Health Organization (WHO). Global tuberculosis report 2014.
[8]	WHO. Fact sheet number 104. Technical report, World Health Organization, Geneva, Switzerland, 2012.
[9]	The patient education institute 1995 – 2012, lnc.www.X-plain.come last reviewed: 10/15/2012.
[10]	Dejen Ketema Mamo and Purnachandra Rao Koya. Mathematical Modeling and Simulation Study of SEIR disease and Data Fitting of Ebola Epidemic in West Africa. Journal of Multidisciplinary Engineering Science and Technology (JMEST). Vol. 2, Issue 1, January 2015, pp 106 – 14. ISSN: 3159 – 0040. http://www.jmest.org/wp-content/uploads/JMESTN42350340.pdf.
[11]	Purnachandra Rao Koya and Dejen Ketema Mamo. Ebola Epidemic Disease: Modelling, Stability Analysis, Spread Control Technique, Simulation Study and Data Fitting. Journal of Multidisciplinary Engineering Science and Technology (JMEST). Vol. 2, Issue 3, March 2015, pp 476 – 84. ISSN: 3159 – 0040. http://www.jmest.org/wp-content/uploads/JMESTN42350548.pdf.
[12]	Abdulsamad Engida Sado and Purnachandra Rao Koya. Application of Brody Growth Function to Describe Dynamics of Breast Cancer Cells. American Journal of Applied Mathematics (AJAM). Vol. 3, No. 3, 2015, pp. 138-145. Doi:10.11648/j.ajam.20150303.20.
[13]	Fekadu Tadege Kobe and Purnachandra Rao Koya. Controlling the Spread of Malaria Disease Using Intervention Strategies. Journal of Multidisciplinary Engineering Science and Technology (JMEST). Vol. 2, Issue 5, May 2015, pp 1068 – 74. ISSN: 3159 – 0040. http://www.jmest.org/wp-content/uploads/JMESTN42350745.pdf.
[14]	WHO. "Tuberculosis (TB)", 2011. http://www.who.int/tb/en
[15]	S. O. Adewale, C.N. Podder and A. B. Gumel, Mathematical analysis of a TB transmission model with DOTS. Canadian Applied mathematics Quarterly, Volume 17, Number 1, spring 2009.
[16]	P. van den Driessche and James Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Mathematical Biosciences 180 (2002) 29-48. www.elsevier.com/locate/mbs.
[17]	A. Ssematimba J. Y. T., Mugisha and L. S. Luboobi, Mathematical Models for the Dynamics of Tuberculosis in Density-dependent Populations: The Case of Internally Displaced Peoples’ Camps (IDPCs) in Uganda. Journal of Mathematics and Statistics 1(3): 217-224, 2005.
[18]	S. Marino and D. Kirschner, The human immune response to the Mycobacterium tuberculosis in lung and lymph node, J. Theor. Biol., 227 (2004), 463-486.

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APA Style

Dancho Desaleng, Purnachandra Rao Koya. (2016). Modeling and Analysis of Malt-Drug Resistance Tuberculosis in Densly Populated Areas. American Journal of Applied Mathematics, 4(1), 1-10. https://doi.org/10.11648/j.ajam.20160401.11

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ACS Style

Dancho Desaleng; Purnachandra Rao Koya. Modeling and Analysis of Malt-Drug Resistance Tuberculosis in Densly Populated Areas. Am. J. Appl. Math. 2016, 4(1), 1-10. doi: 10.11648/j.ajam.20160401.11

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AMA Style

Dancho Desaleng, Purnachandra Rao Koya. Modeling and Analysis of Malt-Drug Resistance Tuberculosis in Densly Populated Areas. Am J Appl Math. 2016;4(1):1-10. doi: 10.11648/j.ajam.20160401.11

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@article{10.11648/j.ajam.20160401.11,
  author = {Dancho Desaleng and Purnachandra Rao Koya},
  title = {Modeling and Analysis of Malt-Drug Resistance Tuberculosis in Densly Populated Areas},
  journal = {American Journal of Applied Mathematics},
  volume = {4},
  number = {1},
  pages = {1-10},
  doi = {10.11648/j.ajam.20160401.11},
  url = {https://doi.org/10.11648/j.ajam.20160401.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20160401.11},
  abstract = {Tuberculosis is an airborne disease caused by the bacterium called mycobacterium tuberculosis. We have compartmentalized the population based on the exposed level to the disease and described the flow using a flowchart. Mathematical model is developed to describe the population dynamics of the compartments. The migration of people from infected class to exposed class, due to failure of continuing the medicine for any reason, is called here as Malt – drug resistance tuberculosis. The equilibrium points identified are disease free, endemic and epidemic. Equilibrium point analysis is made and has been included. Formula for reproduction number is derived. Numerical simulation study of the Mathematical model is conducted using ode45 function of MATLAB software. It is shown that the propagation of the disease is more in the more populated areas and less in the less populated areas.},
 year = {2016}
}

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TY  - JOUR
T1  - Modeling and Analysis of Malt-Drug Resistance Tuberculosis in Densly Populated Areas
AU  - Dancho Desaleng
AU  - Purnachandra Rao Koya
Y1  - 2016/01/04
PY  - 2016
N1  - https://doi.org/10.11648/j.ajam.20160401.11
DO  - 10.11648/j.ajam.20160401.11
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 1
EP  - 10
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20160401.11
AB  - Tuberculosis is an airborne disease caused by the bacterium called mycobacterium tuberculosis. We have compartmentalized the population based on the exposed level to the disease and described the flow using a flowchart. Mathematical model is developed to describe the population dynamics of the compartments. The migration of people from infected class to exposed class, due to failure of continuing the medicine for any reason, is called here as Malt – drug resistance tuberculosis. The equilibrium points identified are disease free, endemic and epidemic. Equilibrium point analysis is made and has been included. Formula for reproduction number is derived. Numerical simulation study of the Mathematical model is conducted using ode45 function of MATLAB software. It is shown that the propagation of the disease is more in the more populated areas and less in the less populated areas.
VL  - 4
IS  - 1
ER  -

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Author Information

Dancho Desaleng

School of Mathematical and Statistical Sciences Hawassa University, Hawassa, Ethiopia
Purnachandra Rao Koya

School of Mathematical and Statistical Sciences Hawassa University, Hawassa, Ethiopia

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APA Style

Dancho Desaleng, Purnachandra Rao Koya. (2016). Modeling and Analysis of Malt-Drug Resistance Tuberculosis in Densly Populated Areas. American Journal of Applied Mathematics, 4(1), 1-10. https://doi.org/10.11648/j.ajam.20160401.11

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ACS Style

Dancho Desaleng; Purnachandra Rao Koya. Modeling and Analysis of Malt-Drug Resistance Tuberculosis in Densly Populated Areas. Am. J. Appl. Math. 2016, 4(1), 1-10. doi: 10.11648/j.ajam.20160401.11

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AMA Style

Dancho Desaleng, Purnachandra Rao Koya. Modeling and Analysis of Malt-Drug Resistance Tuberculosis in Densly Populated Areas. Am J Appl Math. 2016;4(1):1-10. doi: 10.11648/j.ajam.20160401.11

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@article{10.11648/j.ajam.20160401.11,
  author = {Dancho Desaleng and Purnachandra Rao Koya},
  title = {Modeling and Analysis of Malt-Drug Resistance Tuberculosis in Densly Populated Areas},
  journal = {American Journal of Applied Mathematics},
  volume = {4},
  number = {1},
  pages = {1-10},
  doi = {10.11648/j.ajam.20160401.11},
  url = {https://doi.org/10.11648/j.ajam.20160401.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20160401.11},
  abstract = {Tuberculosis is an airborne disease caused by the bacterium called mycobacterium tuberculosis. We have compartmentalized the population based on the exposed level to the disease and described the flow using a flowchart. Mathematical model is developed to describe the population dynamics of the compartments. The migration of people from infected class to exposed class, due to failure of continuing the medicine for any reason, is called here as Malt – drug resistance tuberculosis. The equilibrium points identified are disease free, endemic and epidemic. Equilibrium point analysis is made and has been included. Formula for reproduction number is derived. Numerical simulation study of the Mathematical model is conducted using ode45 function of MATLAB software. It is shown that the propagation of the disease is more in the more populated areas and less in the less populated areas.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - Modeling and Analysis of Malt-Drug Resistance Tuberculosis in Densly Populated Areas
AU  - Dancho Desaleng
AU  - Purnachandra Rao Koya
Y1  - 2016/01/04
PY  - 2016
N1  - https://doi.org/10.11648/j.ajam.20160401.11
DO  - 10.11648/j.ajam.20160401.11
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 1
EP  - 10
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20160401.11
AB  - Tuberculosis is an airborne disease caused by the bacterium called mycobacterium tuberculosis. We have compartmentalized the population based on the exposed level to the disease and described the flow using a flowchart. Mathematical model is developed to describe the population dynamics of the compartments. The migration of people from infected class to exposed class, due to failure of continuing the medicine for any reason, is called here as Malt – drug resistance tuberculosis. The equilibrium points identified are disease free, endemic and epidemic. Equilibrium point analysis is made and has been included. Formula for reproduction number is derived. Numerical simulation study of the Mathematical model is conducted using ode45 function of MATLAB software. It is shown that the propagation of the disease is more in the more populated areas and less in the less populated areas.
VL  - 4
IS  - 1
ER  -

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