Quantifying the effect of demographic stochasticity on the smoking epidemic in the presence of economic stimulus

Smoking, like many other social behaviors, is considered to spread like an epidemic through social interactions among peers. One of the commonly adopted interventions to curb the smoking epidemic is raise in tobacco taxes, which increases the price of cigarettes and makes it less affordable to consume. However, to what extent these interventions affect the spread of smoking behavior is not clearly known. Coupling the spread of smoking behavior with the commonly used interventions such as an increase in the price of cigarettes may offer new insight to control the smoking epidemic. Here, a mathematical model is formulated using differential equations assuming the increase in tax reduces the incidence rate and increases the quitting rate. The model analysis shows that the smoking epidemic has two steady states — smoking free steady-state (SFSS) and smoking endemic steady-state (SESS). The SFSS is stable until SESS exists, whereas the SESS is stable whenever exists. It is found that the smoking epidemic can coexist with economic interventions due to the strong coupling through a feedback loop. As smoking behavior spread amongst the peers, the contacts are mostly restricted to a small group where stochastic nature of social interactions can play a significant role. In view of this, the proposed model is extended to a Markov chain model that embodies the dynamic social contacts. It is found that demographic stochasticity can break the feedback loop between the smoking epidemic and interventions, thereby guarantee the escape from ‘smoking epidemic trap’, even if the parameters for the deterministic model are set within the basin of attraction of the SESS.