Modeling Substance Use Disorder using Deterministic and Stochastic Approaches and A Bayesian Model of Sudden Death

Underlying psychological and biological processes have the potential to negatively affect human health through physical or mental illness. Two such instances include substance use disorders and sudden death events. Substance use disorders are mental health conditions which lead to problematic patterns of substance use, the most severe of which can result in addiction; sudden death refers to death not attributable to trauma, overdose, suicide, or otherwise expected from natural causes. This work leverages mathematical and statistical modeling to uncover important facets of human health not fully understood in medicine.

Substance use epidemiology has recently been an active area of mathematical research; however, new cases of substance use disorder (SUD) have almost exclusively been modeled as the result of an infectious process, neglecting any SUD that was primarily developed in social isolation or due to other risk factors, like mental illness or trauma exposure. The inclusion of non-infectious SUD fundamentally changes model dynamics and should be considered more carefully when determining strategies to reduce addiction in a population. Our primary applications of SUD modeling are in opioid and alcohol use disorders through models with multiple modes of SUD development because of the availability of these drugs and their potential for harm. We used techniques in optimal control theory, ordinary differential equation modeling, and agent-based modeling to analyze the behavior of SUD outside of an infectious disease framework, with an emphasis on how social pressures and individual risk factors contribute to the development of use disorders.

Sudden death has been historically thought to occur more often in the morning. Biological processes, including the release of specific hormones and the regulation of blood pressure and heart rate, support a coronary etiology of sudden death because they are under circadian control. We constructed a Bayesian statistical model using emergency medical data from Wake County, North Carolina to test whether circadian-based physiological factors give rise to a disproportionate number of sudden deaths during the morning. Our results show evidence both for and against this hypothesis depending on the clinical and demographic features of the victims.