Using Physics-Informed Neural Networks to Model the Dynamics of the Opioid Epidemic

The opioid epidemic is one of the fastest growing public health crises in the United States. As a disease that spreads through complex behavior and interaction as opposed to a shared medium, addiction poses a challenge in terms of modeling as it cannot be analyzed through traditional infectious disease frameworks. Previous research struggles to incorporate the dynamic progression of the individual stages of addiction and the differences between medication and endemic-based addiction. In this study, the dynamics of the spreading opioid epidemic are modeled using coupled nonlinear Ordinary Differential Equations (ODEs). These equations employ a compartmental model composed of seven subpopulations including Susceptible, Prescribed, Exposed, Addicted, Deceased, Treated, and Recovered. The model considers the impact of human behavior and interaction of the subpopulations by incorporating both prescription-based addictions and social exposure from addicted individuals. Physics-Informed Neural Networks (PINNs) are used to numerically approximate the parameters for the governing equations based on synthetic data. Additionally, we derive the basic reproduction number to provide further information on the spread of this epidemic. By employing a data-driven interaction-based model, we can more accurately understand the spread of opioid addiction to aid in implementing policies that help mitigate its adverse impacts.