Abstract
In this paper, we are concerned with a delayed smoking model in which the population is divided into five classes. Sufficient conditions guaranteeing the local stability and existence of Hopf bifurcation for the model are established by taking the time delay as a bifurcation parameter and employing the Routh–Hurwitz criteria. Furthermore, direction and stability of the Hopf bifurcation are investigated by applying the center manifold theorem and normal form theory. Finally, computer simulations are implemented to support the analytic results and to analyze the effects of some parameters on the dynamical behavior of the model.
Highlights
In China and around the world, one of the public health problems that has been recognized in recent years is smoking addiction, which has developed into an epidemic causing many deaths
In order to reduce the future effects of smoking on the health of people, the World Health Organization has suggested a set of control policy measures since 2008, known as Framework Convention on Tobacco Control (FCTC)
We incorporate the time delay due to the immunity period, after which the temporarily quit smokers return to the class of smokers, and investigate the following dP(t) dt dS(t) dt
Summary
In China and around the world, one of the public health problems that has been recognized in recent years is smoking addiction, which has developed into an epidemic causing many deaths. In [5], Castullo-Garsow et al formulated a giving up smoking model including three population classes: the potential smokers (P), the smokers (S), and the quit smokers (Q). Rahman et al [14] proposed a giving up smoking model with the continuous age-structure in the chain smokers and studied local and global stability of the model, and the optimal control strategy on potential smokers is presented.
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