Modeling the Opioid Epidemic in Vulnerable Subpopulations and a Multiscale Mixed Modeling Approach to Parasitoid Wasp Dispersal with Host Interaction

The opioid epidemic has severely impacted the United States for decades. A rise in opioid prescriptions during the 1990s led to increased non-medical heroin use and, more recently, fentanyl use. This surge in both prescription and illicit opioids has contributed to a sharp increase in overdoses nationwide. In this study, we present a two-part compartmental model to better understand opioid use and overdose dynamics, focusing on two key factors influencing a vulnerable subpopulation: (1) the overall prevalence of opioid use in the broader community and (2) the availability of targeted resources for the subcommunity. Through mathematical analysis and comparison with population-level data, we assess how different subcommunity scenarios compare to the larger community and how these broader trends influence them.

Parasitoid wasps play a crucial role as agricultural biocontrol agents. However, modeling the spatial movement of these insects is challenging. These wasps are often very small, but their flight is primarily wind-driven, allowing them to travel kilometers from their release point. This results in a complex, multiscale modeling problem. In this study, we build upon an existing mathematical model of parasitoid wasp dispersal to explore the spatial dynamics between the wasps and their hosts. By combining analytical solutions with finite-difference approximations and incorporating half-hourly wind velocity data, we develop a coupled, two-dimensional spatial-temporal model to simulate the dispersal of the parasitoid wasps and their host. We then simulate various scenarios of parasitoid and host dynamics, generating visualizations of their dispersal patterns over time across a field. These simulations offer valuable insights into the complex interactions between the wasps and their hosts, advancing our understanding of their dispersal behavior and the potential for biocontrol applications.