Adolescent vaping behaviours: Exploring the dynamics of a social contagion model

Vaping, or the use of electronic cigarettes (e-cigarettes), is an ongoing issue for public health. The rapid increase in e-cigarette usage, particularly among adolescents, has often been referred to as an epidemic. Drawing upon this epidemiological analogy between vaping and infectious diseases as a theoretical framework, we present a deterministic compartmental model of adolescent e-cigarette smoking which accounts for social influences on initiation, relapse, and cessation behaviours. We use results from a sensitivity analysis of the model's parameters on various response variables to identify key influences on system dynamics and simplify the model into one that can be analysed more thoroughly. We identify a single feasible endemic equilibrium for the proportion of smokers that decreases as social influence on cessation increases. Through steady state and stability analyses, as well as simulations of the model, we conclude that social influences from and on temporary quitters are not important in overall model dynamics, and that social influences from permanent quitters can have a significant impact on long-term system dynamics. In particular, we show that social influence on cessation can induce persistent recurrent smoking outbreaks.