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

Area of Science:

• Mathematical modeling
• Sociological dynamics
• Epidemiology

Background:

• Mathematical models are established metaphors for biological and epidemiological systems.
• Epidemic modeling frameworks have been applied to sociological phenomena driven by peer pressure.
• Numerous dynamical systems research projects have explored these applications.

Purpose of the Study:

• To review existing studies applying epidemic modeling to sociology.
• To identify common structures in these interdisciplinary applications.
• To introduce a new mathematical metaphor for hierarchical phenomena persistence.

Main Methods:

• Review of dynamical systems research projects.
• Analysis of common structures in sociological and epidemiological models.
• Identification of multiple nonlinearities and thresholds.

Main Results:

• Established phenomena can persist under conditions where they could not initially emerge (backward bifurcation).
• A new mathematical metaphor using multiple nonlinearities is proposed.
• The metaphor describes multiple thresholds governing hierarchical phenomena.

Conclusions:

• Mathematical metaphors offer insights into complex sociological and epidemiological systems.
• Understanding thresholds is crucial for predicting the persistence of phenomena.
• The concept of backward bifurcation has implications beyond epidemiology.