The Effect of Smoking Behavior in the Human Population Growth of Lung Cancer Patients

Lu’luul Wardah, Trisilowati Trisilowati, Wuryansari Muharini Kusumawinahyu

Abstract


This article discusses a model of lung cancer as the effect of smoking behavior on both active and passive smoker. There are four subpopulations in this model, namely susceptible subpopulation, active smoker subpopulation, passive smoker subpopulation, and subpopulation of lung cancer.  Dynamical analysis is conducted to determine the equilibrium point, existence condition for equilibrium point, and analyze their stability. Based on analysis result, there are three equilibrium points. First equilibrium point shows that all subpopulations extinct. Second equilibrium point shows that only susceptible subpopulation can survive, and the last equilibrium point shows that all subpopulations can survive. First equilibrium point always exists while the others exist under certain condition. The stability of first equilibrium point can be reached when the intrinsic growth rate is less than the death rate. Whereas, the others equilibrium points will be stable under certain condition. Numerical simulation is performed to illustrate the analysis result. It is shown that numerical results are in accordance with analysis result. These numerical simulations also indicate that the rate of passive smoker plays important role in the growth rate of lung cancer.


Keywords


dynamical analysis, active smokers, passive smokers, lung cancer

Full Text:

PDF

References


WHO, “Media Center: Cancer,” World Health Organization, 2016. [Daring]. Tersedia pada: http://www.who.int/mediacentre/factsheets/fs297/en/. [Diakses: 21-Apr-2016].

A. T. O. Sari, N. Ramdhani, dan M. Eliza, “Empati dan perilaku merokok di tempat umum,” J. Psikol., vol. 30, no. 2, hal. 81–90, 2003.

T. Y. Aditama, Rokok dan Kesehatan. Jakarta: UI Press, 2007.

S. C. Darby dan M. C. Pike, “Lung cancer and passive smoking: predicted effects from a mathematical model for cigarette smoking and lung cancer.,” Br. J. Cancer, vol. 58, no. 6, hal. 825–31, Des 1988.

R. Taylor, F. Najafi, dan A. Dobson, “Meta-analysis of studies of passive smoking and lung cancer: effects of study type and continent.,” Int. J. Epidemiol., vol. 36, no. 5, hal. 1048–59, Okt 2007.

J. N. Andest, “A Mathematical Model on Cigarette Smoking And Nicotine In The Lung,” IRJES, vol. 2, no. 6, hal. 1–3, 2013.

R. W. Hndoosh, S. Kumar, dan M. S. Saroa, “Fuzzy mathematical models for the analysis of fuzzy systems with application to liver disorders,” IOSR J. Comput. Eng., vol. 16, no. 5, hal. 71–85, 2014.

H. Namazi dan M. Kiminezhadmalaie, “Diagnosis of Lung Cancer by Fractal Analysis of Damaged DNA.,” Comput. Math. Methods Med., vol. 2015, hal. 1–11, 2015.

C. A. Acevedo-Estephania, C. Gonzalez, K. R. Rios-Soto, dan E. D. Summerville, “A Mathematical Model for Lung Cancer: The Effects of Second-hand Smoke and Education,” 2000.

G. P. Samanta, “Dynamic Behaviour for a Nonautonomous Smoking Dynamical Model with Distributed Time Delay,” J. Appl. Math. Informatics, vol. 29, no. 3–4, hal. 721–741, 2011.

I. Sutantiati, “Analisis Dinamik Model Penyakit Kanker Paru-paru Akibat Pengaruh Perilaku Merokok,” Universitas Brawijaya, 2016.

F. Brauer dan C. Castillo-Chavez, Mathematical Models in Population Biology and Epidemiology Volume 40 of Texts in Applied Mathematics, 2nd ed. New York: Springer Science & Business Media, 2010.


Refbacks

  • There are currently no refbacks.