Dynamics of a smoking model with smoking death rate

In this work, we derive and analyze a smoking model by taking into account hospitalized smokers and smoke quitters of two types: temporary and permanent, which is one of the possible extensions of the giving-up smoking model. Temporary quitters may become smokers again, while permanent quitters, once they quit, never smoke again in the entire life span. The existence and stability of the possible equilibria of the model are examined in terms of a certain threshold condition ${\mathcal R}$, the smoking generation number (the basic reproduction number). Numerical simulations are carried out to investigate the influence of the key parameters on the spread of smoking, to support the analytical conclusion and illustrate possible behavioral scenarios.