### Mathematical Biosciences and Engineering

2013, Issue 5&6: 1587-1607. doi: 10.3934/mbe.2013.10.1587

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

• Received: 01 August 2012 Accepted: 29 June 2018 Published: 01 August 2013
• MSC : Primary: 91D99, 91E99; Secondary: 92D25.

• 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.

Citation: Christopher M. Kribs-Zaleta. Sociological phenomena as multiple nonlinearities: MTBI's new metaphor for complex human interactions[J]. Mathematical Biosciences and Engineering, 2013, 10(5&6): 1587-1607. doi: 10.3934/mbe.2013.10.1587

### Related Papers:

• 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.

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