Spreading Dynamic of a PLSGP Giving up Smoking Model on Scale-Free Network

Abstract

A new PLSGP (potential smokers-light smokers-persistent smokers-giving up smokers-potential smokers) model with birth and death rates on complex heterogeneous networks is presented. Using the mean-field theory, we obtain the basic reproduction number 0 R and find that basic reproduction number for constant contact is independent of the topology of the underlying networks. When 0 1 R < , the smoking-free equilibrium is globally asymptotically stable, then the smoking will disappear. When 0 1 R > , the smoking-present equilibrium is global attractivity, then the number of smoker will remain stable and smoking will become endemic. Numerical simulations illustrated theoretical results. Our result shows that the model is very important to control the spread of the smoking.

Dynamical analysis of a giving up smoking model with time delay

“…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 also presented. Fei and Liu [15] presented a giving up smoking model with birth and death rates on complex heterogeneous networks. They examined the stability and attractivity of the proposed model.…”