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Worldwide, smoking is a common social practice, especially in places like schools and on important occasions. The World Health Organization (WHO) states that smoking is the third leading cause of death worldwide and the most significant avoidable cause of disease. Thus in this study, we present the solution behavior of the fractal-fractional (FF) smoking model. Using an effective numerical integration technique, the discretized system of FF differential equations that results is numerically integrated. By using RK4 to evaluate the numerical solution, we can meet the requirements for both efficiency and accuracy in the given approach. In the hope of providing some recommendations through which to reduce the risks of this bad behavior, the effect of some parameters and external factors affecting the solution behavior of this proposed mathematical model was studied, including the recruitment rate (due to immigration or birth) and the smoking cessation rate. The results show that the implemented technique is a straightforward and efficient tool for modeling the solution for these models.

The social habit of smoking has affected the whole world in a social manner. It is the main cause of diseases like cancers, asthma, bad breath, etc., and a source of spreading of infectious diseases like COVID-19. This work is related to an existing smoking model with relapse habit converted in fractional order. First, formulation of fractional-order smoking model is presented and then the dynamics of proposed problem is analyzed. Fixed-point theory via Banach contraction and Schauder theorems is used to derive the existence and uniqueness of the model. At last, the adaptive predictor–corrector algorithm and Runge–Kutta fourth-order (RK4) strategy are used to perform simulation. To bolster the validity of the theoretical results, a set of numerical simulations are performed. A good agreement between hypothetical and numerical results is demonstrated via numerical simulations using MATLAB software.

Smoking poses an enormous threat to public health in the globe and continues to be one of the main cause of health problems. In this paper, a delayed smoking model with reversion class is proposed. Local stability of the smoking equilibrium and Hopf bifurcation is analyzed by taking the time delay as the bifurcation parameter. In particular, global exponential stability is proved by using the linear matrix inequality method. The theoretical results obtained are validated numerically and graphically.

Smoking has many harmful effects due to its toxic chemicals, which cause serious diseases. Our major interest in this research is to formulate a spatiotemporal mathematical model that predicts the evolution of smoking in society using a mathematical model that includes the large mobility of individuals. Indeed, we are concerned to study the global asymptotic stability of the unique positive steady state related to this model. The principal objective of this paper is to show that the smoking has no threshold dynamics as it has been shown for a large sample of epidemic models, and the consumption of cigarettes is always persistent, and based on the assumption of the parameters that verify the Lipschitz condition. We proved that the investigated model is always persistent and the unique positive equilibrium state is always globally stable. The mathematical finding is supported numerically using numerical simulations.

This work considers a generalized fuzzy fractional smoking model with Caputo $gH$-types fractional derivatives upon considering the case of uncertainty quantification. The disease-free equilibrium point and stability of the equilibrium point have been discussed for the fuzzy nonlinear fractional smoking model. The analytical proofs for the existence and uniqueness of the proposed model are concerned with the help of the fixed-point theorem, Banach contraction, and Schauder theorem. A robust double parametric approach with a generalized transform is used to study the behavior of the fuzzy fractional model in an uncertain context and obtain the convergence analysis of the study in a crisp context. Finally, the obtained results of the proposed model have been validated with the Runge–Kutta method of fourth order in crisp case $(\varsigma =1,\ell =0)$.