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When a pathogen enters the body and reproduces, it can cause an infection, damage body cells, and cause illness symptoms that eventually lead to disease. Therefore, its prevention requires breaking the chain of infection.
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Transmission-based precautions are for patients known to be infected or suspected to be infected or colonized with organisms that pose a significant risk to others. Some transmission-based precautions include contact, enteric, and droplet.
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Related Experiment Video

Updated: Mar 6, 2026

A New Method for Inducing a Depression-Like Behavior in Rats
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Critical Behaviors in Contagion Dynamics.

L Böttcher1, J Nagler1, H J Herrmann1

  • 1ETH Zurich, Wolfgang-Pauli-Strasse 27, CH-8093 Zurich, Switzerland.

Physical Review Letters
|March 11, 2017
PubMed
Summary

This study unifies complex contagion dynamics, revealing three universal critical regimes: uncorrelated spontaneous transitions, contact processes, and cusp catastrophes. This research deepens the mathematical understanding of system behavior.

Area of Science:

  • Complex systems science
  • Statistical physics
  • Network science

Background:

  • Contagion models describe state transitions in networks.
  • Previous models lacked a unifying framework for diverse dynamics.
  • Understanding critical behavior is key to predicting system-level changes.

Purpose of the Study:

  • To develop a unifying mean-field theory for general contagion models.
  • To identify the universal critical regimes governing these dynamics.
  • To resolve long-standing debates on contagion universality classes.

Main Methods:

  • Derivation of a unifying mean-field theory.
  • Analytical investigation of system dynamics.
  • Characterization of state transitions (spontaneous, neighbor-induced, reverse).

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Main Results:

  • Identified three distinct critical regimes: uncorrelated spontaneous transition dynamics, contact process dynamics, and cusp catastrophes.
  • Demonstrated that these three regimes encompass all possible critical behaviors.
  • Showcased rich dynamics including limit cycles and random phase switching.

Conclusions:

  • The critical behavior of general contagion models is limited to three universal regimes.
  • The derived mean-field theory provides a comprehensive mathematical understanding.
  • This work resolves debates on universality classes in complex contagion dynamics.