Numerical investigation of smoking behavior dynamics using the spectral collocation method

Smoking poses a significant threat to global public health and remains one of the leading causes of health problems. To examine these smoking-related issues, this paper aims to study the modified smoking model, which represents a five-compartment system consisting of potential smokers, snuffing class, irregular smokers, regular smokers, and quitters. The model is evaluated computationally using the spectral collocation method. The core idea of the spectral collocation technique is to approximate the solution as a truncated series of basis functions using Chebyshev polynomials. By incorporating collocation points, the truncated series is transformed into an operational matrix form, which in turn converts the governing differential equations into a system of non-linear algebraic equations. Furthermore, the residual and absolute error for different collocation points are established. Additionally, the effects of various parameters such as transmission rate, recovery rate, quit rate, and death rate on the smoking model have been analyzed. All these computational investigations on the model are displayed in the form of figures. Finally, the effect of different combinations of parameters on the smoking dynamics and its impact is represented using contour plots.

کلیدواژه ها:

Spectral collocation method ، Smoking Model ، Chebyshev polynomial