Mathematical Models of Bipolar Disorder

I've blogged about this paper multiple times before---including discussions of a very snarky letter-to-the-editor that my colleague and I wrote.

The paper itself has now been assigned its official journal volume, number, and page numbers. You can find the article here.


Title: Mathematical Models of Bipolar Disorder

Authors: Darryl Daugherty, Tairi Roque-Urrea, John Urrea-Roque, Jessica Troyer, Stephen Wirkus, and Mason A. Porter

Abstract: We use limit cycle oscillators to model bipolar II disorder, which is characterized by alternating hypomanic and depressive episodes and afflicts about 1% of the United States adult population. We consider two non-linear oscillator models of a single bipolar patient. In both frameworks, we begin with an untreated individual and examine the mathematical
effects and resulting biological consequences of treatment. We also briefly consider the dynamics of interacting bipolar II individuals using weakly-coupled, weakly-damped harmonic oscillators. We discuss how the proposed models can be used as a framework for refined models that incorporate additional biological data. We conclude with a discussion of possible generalizations of our work, as there are several biologically-motivated extensions that can be readily incorporated into the series of models presented here.