Mathematical Biology Seminar - David White

David White, Department of Mathematics, Denison University

Modeling the Opioid Epidemic in Space and Time

I will give an overview of several papers about statistical and mathematical models for drug overdose, and how they can be used to save lives. I will first explain the basics of time series analysis and how time series models can create an “early warning system,” using law-enforcement drug seizure data to predict changes in overdose deaths. I will then turn to the spatial structure of the epidemic, viewing it as a spatiotemporal dynamical system and trying to predict local spikes. I will explain traditional statistical tools for this problem, and where those tools fall short. To remedy that, I will introduce some ideas from topological data analysis, including Mapper, persistent homology, and vineyards. In recent joint work with Nick Bermingham and Nathan Willey, we use vineyards to follow persistent features through time and to forecast future changes in the geography of overdose mortality. Along the way I will emphasize connections with familiar ideas from statistical modeling, time series, spatial statistics, and dynamical systems, and I will provide several open problems and a road map to a collection of freely available and underutilized datasets where even relatively simple analyses would be impactful. The talk assumes only a basic knowledge of statistics and no previous knowledge of topological data analysis. Students are welcome.