Mathematical Models of Bipolar Disorder

TL;DR

This paper develops mathematical models using limit cycle oscillators to simulate Bipolar II disorder, exploring untreated and treated states, and interactions between individuals, aiming to enhance understanding and future modeling of the disorder.

Contribution

Introduces two nonlinear oscillator models for Bipolar II disorder and examines effects of treatment and interactions, providing a foundation for more detailed biological modeling.

Findings

Models replicate bipolar episode dynamics

Treatment effects alter oscillator behavior

Interpersonal interactions influence disorder dynamics

Abstract

We use limit cycle oscillators to model Bipolar II disorder, which is characterized by alternating hypomanic and depressive episodes and afflicts about one percent of the United States adult population. We consider two nonlinear 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.