A Risk-Structured Model of the Influence of Mental Health on Opioid Addiction.

In 2021, over 80,000 of the 107,622 overdose deaths in the United States involved opioids, with opioid use disorder (OUD) and fatal overdoses imposing economic costs exceeding $1 trillion in 2017. Mathematical modeling provides an important tool for understanding the dynamics of the opioid epidemic and evaluating the potential benefits of different treatment and prevention strategies. In particular, we extend the Susceptible-Infected-Recovered paradigm for modeling infectious diseases to the opioid crisis. While existing compartmental models of OUD often assume equal risk of addiction across individuals, this assumption overlooks the significant role of risk heterogeneity. Unlike previous models that assume uniform addiction risk, our model incorporates risk stratification to account for the disproportionate burden among individuals with mental health disorders, who represent 20% of the U.S. population but account for over half of opioid prescriptions and misuse. Our compartmental model distinguishes between addiction pathways initiated by prescription opioids and those driven by social influences. Using existing data, we calibrate the model to estimate key parameters and quantify the impact of risk heterogeneity, offering insights to the addiction process.