E-cigarette smoking with peer pressure

A model is presented involving non-smokers, tobacco cigarette smokers, and those who smoke electronic cigarettes. The transfer from the tobacco smoker class to the e-cigarette class is via a peer pressure term. It is shown that there are three distinct equilibria. One involves no smokers of any kind. A second has only non-smokers and smokers of tobacco cigarettes. The third has a steady state with all three categories. Conditions are derived under which each equilibrium state will be stable. Numerical simulations are given that show the convergence to steady state for the third equilibrium. Simulations are also performed for a more general model where the peer pressure term in the tobacco to e-cigarette transition involves also a conformity bias.