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

Lu’luul Wardah, Trisilowati Trisilowati, Wuryansari Muharini Kusumawinahyu


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.


dynamical analysis, active smokers, passive smokers, lung cancer

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