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Universal behavior in a generalized model of contagion
Peter Sheridan Dodds1, Duncan J Watts
1Institute for Social and Economic Research and Policy, Columbia University, 420 West 118th Street, New York, New York 10027, USA. peter.dodds@columbia.edu
Physical Review Letters
|July 13, 2004
Summary
This study introduces a general contagion model that incorporates memory of past exposures. The model reveals three distinct collective dynamics, offering new ways to assess and influence contagion events.
Area of Science:
- Mathematical modeling
- Epidemiology
- Social sciences
Background:
- Contagion models are widely used in biological and social sciences.
- Existing models do not fully capture the nuances of exposure memory.
Purpose of the Study:
- Introduce a general contagion model incorporating exposure memory.
- Analyze the collective dynamics and parameters influencing contagion.
- Propose methods for assessing and controlling contagion events.
Main Methods:
- Developed a general mathematical model for contagion.
- Incorporated memory of past exposures into the model.
- Derived exact solutions for a simplified version of the model.
Main Results:
- The model interpolates between existing contagion models.
- Identified three fundamental classes of collective dynamics.
- Showed that two parameters determine system dynamics for a given memory length.
Conclusions:
- The generalized contagion model provides a unified framework.
- Novel measures can assess population susceptibility to contagion.
- The model offers strategies to inhibit or facilitate contagion spread.