The Mathematical Institute, University of Oxford, Eprints Archive

Mathematical models of bipolar disorder

Daugherty, D and Roque-Urrea, T and Urrea-Roque, J and Troyer, J and Wirkus, S and Porter, M A (2009) Mathematical models of bipolar disorder. Communications in Nonlinear Science and Numerical Simulations, 14 (7). pp. 2897-2908.

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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.

Item Type:Article
Uncontrolled Keywords:Bipolar disorder; Limit cycle oscillators; Lienard oscillators; Averaging
Subjects:A - C > Biology and other natural sciences
Research Groups:Centre for Mathematical Biology
ID Code:1813
Deposited By: Sara Jolliffe
Deposited On:27 Feb 2014 08:40
Last Modified:29 May 2015 19:30

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