Keywords: System Dynamics, Ito Calculus, Mean Field Theory, Stochastic Differential Equations, Ordinary Differential Equations, Tobacco-use model
Conventional tobacco use System Dynamics (SD) models typically employ either a system of ordinary differential equations (ODEs), or Markov transition models to describe population dynamics. Using ODEs implies that the input/output relationship of an SD model is deterministic, and so, is unable to properly capture any stochastic shocks to the system, and all model outputs are smooth, deterministic, and well-behaved. A Markov model implies that any stochastic shocks come strictly from the estimation of transition probabilities. When a stochastic shock is present, solutions to stochastic differential equations have extra diffusion terms not present in ODE solutions, and so, a different approach is needed. In this paper a novel stochastic system dynamics model to project the impact of regulatory policy on the US population is proposed. Using Itô calculus, the stochastic transition rates are modeled with Cox-Ingersoll-Ross processes, properly capturing the effect of the disturbances, and path dependence mechanisms are introduced to capture the various transitions from initiation to addiction. The validated model is shown to reduce to the conventional SD model under simple assumptions