While substance use epidemiology has been an active area of mathematical research in recent years, the social and mental processes that are involved in the development of substance use disorders have presented challenges to advancing the epidemiological theory and how they differ from the contraction of pathogenic disease. Such distinction is especially pertinent in the context of the current United States opioid epidemic and its intersection with the recent COVID-19 pandemic, as both prescription drugs and social influence play major roles in the development of opioid use disorder. In this paper, we construct a stochastic network model to explore how individual-level interactions give rise to population-level dynamics. To do so, we propose a novel minimization algorithm informed by a sensitivity analysis to heuristically fit a stochastic network model to deterministic time series data, a problem that has received little attention in the literature and involves significant hurdles related to computational cost. The method adds to existing tools like Nelder-Mead or Powell's method for when gradient-based optimization methods are infeasible, and allows us to quantify the change in the social spread of opioid use disorder among current drug users when the population is not well-mixed. Our results suggest that the proposed algorithm is strongly robust to changes in the initial parameterization and that existing social structures likely play a prominent role in the mechanisms behind illicit opioid use, highlighting the need for continued study on individual-level opioid dynamics in small communities.
Pearcy et al. (Wed,) studied this question.