Data-Informed Modeling in the Health Sciences

The adoption of automation and technology by health professionals is triggering an explosion of databases and data streams in that sector. The emergence of this data torrent creates the pressing need to mine it for value, which in turn requires investment for the development of modeling and analysis tools. In view of this, dynamicists are presented with the terrific opportunity to enrich their discipline by supplying it with new tools, expanding its scope, and elevating its social impact. This chapter is written in that spirit, examining three concrete case studies encountered in the field: quantifying the salmonellosis risk posed by distinct food sources, assimilating genetic data into a dynamical model for avian influenza transmission, and statistically decontaminating gas chromatography/mass spectroscopy time series. We review available prototypical models and build on them guided by data and mathematical abstraction, demonstrating in the process how to root a model into data. This takes us quite naturally into the realm of probabilistic and statistical modeling and reopens a decades-old discussion on the role of discrete models in applied mathematics. We also touch briefly on the timely subject of mathematicians being employed as such outside math departments and attempt a short outlook on their prospects and opportunities.