Smoking as Epidemic: Modeling and Simulation Study

Sintayehu Agegnehu Matintu

doi:doi:10.11648/j.ajam.20170501.14

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Smoking as Epidemic: Modeling and Simulation Study

Sintayehu Agegnehu Matintu

Published in American Journal of Applied Mathematics (Volume 5, Issue 1)

Received: 4 December 2016 Accepted: 23 December 2016 Published: 23 February 2017

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Abstract

In this paper we propose smoking epidemic model which analyzes the spread of smoking in a population. The model consists of five compartments corresponding to five population classes, namely, potential-moderate-heavy-temporarily recovered- permanently recovered class. The basic reproduction number R₀ has been derived, and then the dynamical behaviors of both smoking free equilibrium and smoking persistent equilibrium are analyzed by the theory of differential equation, and Numerical simulation has been carried out and the results have confirmed the verification of analytical results. Sensitivity analysis of R₀ identifies β₁, the transmission coefficient from potential smokers to moderate smokers and β₂, the transmission coefficient from potential smokers to heavy smokers, as the most useful parameters to target for the reduction of R₀.

Published in	American Journal of Applied Mathematics (Volume 5, Issue 1)
DOI	10.11648/j.ajam.20170501.14
Page(s)	31-38
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

Smoking Model, Reproduction Number, Equilibrium Value, Stability, Sensitivity Analysis, Numerical Simulation

References

[1]	http://en.wikipedia.org/wiki/Smoking (3^th October, 2016)
[2]	https://en.wikipedia.org/wiki/Epidemiology (17^th November, 2016)
[3]	C. Castillo-Garsow, G. Jordan-Salivia, and A. Rodriguez Herrera, Mathematical models for the dynamics of tobacco use, recovery, and relapse, Technical Report Series BU-1505-M, Cornell University, Ithaca, NY, USA, 1997.
[4]	O. Sharomi, A. B. Gumel, Curtailing smoking dynamics: A mathematical modeling approach, Applied Mathematics and Computation 195 (2008) 475–499.
[5]	G. Zaman, Qualitative behavior of giving up smoking model; Bulletin of the Malaysian Mathematical Sciences Society (2) (2011) 403-415.
[6]	Z. Alkhudhari, S. Al-Sheikh, S. Al-Tuwairqi, Global Dynamics of a Mathematical Model on Smoking, ISRN Applied Mathematics vol. (2014), Article ID 847075.
[7]	Z. Alkhudhari, S. Al-Sheikh, S. Al-Tuwairqi, The effect of occasional smokers on the dynamics of a smoking model, International Mathematical Forum, 9, No. 25 (2014), 1207- 1222.
[8]	Z. Alkhudhari, S. Al-Sheikh, S. Al-Tuwairqi, The effect of heavy smokers on the dynamics of a smoking model, International Journal of Differential Equations and Applications, 14, No. 4 (2015), 1311-2872.
[9]	B. Benedict, Modeling Alcoholism as a Contagious Disease: How “Infected” Drinking Buddies Spread Problem Drinking. SIAM News, Vol. 40, No. 3, 2007.
[10]	P. van den Driessche, J. Watmough, Reproduction numbers and sub-thershold endemic equalibria for compartmental models of disease transmission, Math. Biosci. 180 (2002) 29–48.
[11]	G. Zaman, Y. H. Kang, and I. H. Jung, “Stability analysis and optimal vaccination of an SIR epidemic model,” BioSystems, vol. 93, no. 3, pp. 240–249, 2008.
[12]	American National Institute of Drug Abuse, “Cigarettes and Other Nicotine Products,” http://www.nida.nih.gov/pdf/ infofacts/Nicotine04.pdf.
[13]	L. Arriola, J. Hyman, Lecture notes, Forward and adjoint sensitivity analysis: with applications in Dynamical Systems, Linear Algebra and Optimization, Mathematical and Theoretical Biology Institute, Summer, 2005.
[14]	Z. Alkhudhari, S. Al-Sheikh, S. Al-Tuwairqi, Global Dynamics of a Mathematical Model on Smoking, ISRN Applied Mathematics vol. (2014), Article ID 847075.
[15]	L. Edelstein Keshet, Mathematical Models in Biology. Random House, New York, 1988. SIAM edition.

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Sintayehu Agegnehu Matintu. (2017). Smoking as Epidemic: Modeling and Simulation Study. American Journal of Applied Mathematics, 5(1), 31-38. https://doi.org/10.11648/j.ajam.20170501.14

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ACS Style

Sintayehu Agegnehu Matintu. Smoking as Epidemic: Modeling and Simulation Study. Am. J. Appl. Math. 2017, 5(1), 31-38. doi: 10.11648/j.ajam.20170501.14

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AMA Style

Sintayehu Agegnehu Matintu. Smoking as Epidemic: Modeling and Simulation Study. Am J Appl Math. 2017;5(1):31-38. doi: 10.11648/j.ajam.20170501.14

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@article{10.11648/j.ajam.20170501.14,
  author = {Sintayehu Agegnehu Matintu},
  title = {Smoking as Epidemic: Modeling and Simulation Study},
  journal = {American Journal of Applied Mathematics},
  volume = {5},
  number = {1},
  pages = {31-38},
  doi = {10.11648/j.ajam.20170501.14},
  url = {https://doi.org/10.11648/j.ajam.20170501.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20170501.14},
  abstract = {In this paper we propose smoking epidemic model which analyzes the spread of smoking in a population. The model consists of five compartments corresponding to five population classes, namely, potential-moderate-heavy-temporarily recovered- permanently recovered class. The basic reproduction number R0 has been derived, and then the dynamical behaviors of both smoking free equilibrium and smoking persistent equilibrium are analyzed by the theory of differential equation, and Numerical simulation has been carried out and the results have confirmed the verification of analytical results. Sensitivity analysis of R0 identifies β1, the transmission coefficient from potential smokers to moderate smokers and β2, the transmission coefficient from potential smokers to heavy smokers, as the most useful parameters to target for the reduction of R0.},
 year = {2017}
}

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TY  - JOUR
T1  - Smoking as Epidemic: Modeling and Simulation Study
AU  - Sintayehu Agegnehu Matintu
Y1  - 2017/02/23
PY  - 2017
N1  - https://doi.org/10.11648/j.ajam.20170501.14
DO  - 10.11648/j.ajam.20170501.14
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 31
EP  - 38
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20170501.14
AB  - In this paper we propose smoking epidemic model which analyzes the spread of smoking in a population. The model consists of five compartments corresponding to five population classes, namely, potential-moderate-heavy-temporarily recovered- permanently recovered class. The basic reproduction number R0 has been derived, and then the dynamical behaviors of both smoking free equilibrium and smoking persistent equilibrium are analyzed by the theory of differential equation, and Numerical simulation has been carried out and the results have confirmed the verification of analytical results. Sensitivity analysis of R0 identifies β1, the transmission coefficient from potential smokers to moderate smokers and β2, the transmission coefficient from potential smokers to heavy smokers, as the most useful parameters to target for the reduction of R0.
VL  - 5
IS  - 1
ER  -

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Author Information

Sintayehu Agegnehu Matintu

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

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APA Style

Sintayehu Agegnehu Matintu. (2017). Smoking as Epidemic: Modeling and Simulation Study. American Journal of Applied Mathematics, 5(1), 31-38. https://doi.org/10.11648/j.ajam.20170501.14

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ACS Style

Sintayehu Agegnehu Matintu. Smoking as Epidemic: Modeling and Simulation Study. Am. J. Appl. Math. 2017, 5(1), 31-38. doi: 10.11648/j.ajam.20170501.14

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AMA Style

Sintayehu Agegnehu Matintu. Smoking as Epidemic: Modeling and Simulation Study. Am J Appl Math. 2017;5(1):31-38. doi: 10.11648/j.ajam.20170501.14

Copy | Download

@article{10.11648/j.ajam.20170501.14,
  author = {Sintayehu Agegnehu Matintu},
  title = {Smoking as Epidemic: Modeling and Simulation Study},
  journal = {American Journal of Applied Mathematics},
  volume = {5},
  number = {1},
  pages = {31-38},
  doi = {10.11648/j.ajam.20170501.14},
  url = {https://doi.org/10.11648/j.ajam.20170501.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20170501.14},
  abstract = {In this paper we propose smoking epidemic model which analyzes the spread of smoking in a population. The model consists of five compartments corresponding to five population classes, namely, potential-moderate-heavy-temporarily recovered- permanently recovered class. The basic reproduction number R0 has been derived, and then the dynamical behaviors of both smoking free equilibrium and smoking persistent equilibrium are analyzed by the theory of differential equation, and Numerical simulation has been carried out and the results have confirmed the verification of analytical results. Sensitivity analysis of R0 identifies β1, the transmission coefficient from potential smokers to moderate smokers and β2, the transmission coefficient from potential smokers to heavy smokers, as the most useful parameters to target for the reduction of R0.},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - Smoking as Epidemic: Modeling and Simulation Study
AU  - Sintayehu Agegnehu Matintu
Y1  - 2017/02/23
PY  - 2017
N1  - https://doi.org/10.11648/j.ajam.20170501.14
DO  - 10.11648/j.ajam.20170501.14
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 31
EP  - 38
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20170501.14
AB  - In this paper we propose smoking epidemic model which analyzes the spread of smoking in a population. The model consists of five compartments corresponding to five population classes, namely, potential-moderate-heavy-temporarily recovered- permanently recovered class. The basic reproduction number R0 has been derived, and then the dynamical behaviors of both smoking free equilibrium and smoking persistent equilibrium are analyzed by the theory of differential equation, and Numerical simulation has been carried out and the results have confirmed the verification of analytical results. Sensitivity analysis of R0 identifies β1, the transmission coefficient from potential smokers to moderate smokers and β2, the transmission coefficient from potential smokers to heavy smokers, as the most useful parameters to target for the reduction of R0.
VL  - 5
IS  - 1
ER  -

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