Mathematical Biosciences and Engineering (MBE)

Sociological phenomena as multiple nonlinearities: MTBI's new metaphor for complex human interactions

Pages: 1587 - 1607, Volume 10, Issue 5/6, October/December 2013      doi:10.3934/mbe.2013.10.1587

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Christopher M. Kribs-Zaleta - Mathematics Department, University of Texas at Arlington, Box 19408, Arlington, TX 76019-0408, United States (email)

Abstract: Mathematical models are well-established as metaphors for biological and epidemiological systems. The framework of epidemic modeling has also been applied to sociological phenomena driven by peer pressure, notably in two dozen dynamical systems research projects developed through the Mathematical and Theoretical Biology Institute, and popularized by authors such as Gladwell (2000). This article reviews these studies and their common structures, and identifies a new mathematical metaphor which uses multiple nonlinearities to describe the multiple thresholds governing the persistence of hierarchical phenomena, including the situation termed a ``backward bifurcation'' in mathematical epidemiology, where established phenomena can persist in circumstances under which the phenomena could not initially emerge.

Keywords:  Backward bifurcation, multiple nonlinearities, dynamical systems, epidemic, metaphor.
Mathematics Subject Classification:  Primary: 91D99, 91E99; Secondary: 92D25.

Received: August 2012;      Accepted: March 2013;      Available Online: August 2013.