The Influence of Time Delay and Gaussian White Noise on the Dynamics of Tobacco Smoking Model

This article analyses the influence of psychological and social addictions such as drug and tobacco consumption problems on humans by using an appropriate nonlinear computational formulation. We propose a mathematical model to simulate the multiple stages and behaviors of the smoking addiction process. Firstly, we present the dynamics of the local and global stability of the tobacco smoking model at existing equilibrium points and discuss the Hopf-Bifurcation analysis of the delayed model by regarding the time delay as a bifurcation parameter and derive specific formulas for the stability and direction of the Hopf bifurcation employing the normal form theory and centre manifold theorem. Then, we enhance our delayed model by considering the effects of the social environment. Precisely, we incorporate additive white noises into our delayed system to simulate the stochastic factors. Then, we analytically present some statistical properties of the perturbed system. Finally, we performed the sensitivity analysis and some numerical examples to discuss the feasibility of our theoretical findings.