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Simple model of epidemics with pathogen mutation.

Michelle Girvan1, Duncan S Callaway, M E J Newman

  • 1Department of Physics, Cornell University, Ithaca, New York 14853-2501, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 23, 2002
PubMed
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Pathogen mutation and immune memory significantly influence epidemic dynamics. Rapid mutation is crucial for pathogen survival in highly connected populations to overcome immune responses.

Area of Science:

  • Epidemiology
  • Immunology
  • Mathematical Biology

Background:

  • The dynamics of infectious diseases are shaped by pathogen evolution and host immune responses.
  • Understanding the interplay between pathogen mutation and immune memory is crucial for predicting epidemic behavior.

Purpose of the Study:

  • To investigate how pathogen mutation and immune memory affect epidemic dynamics.
  • To analyze two related mathematical models simulating these interactions.

Main Methods:

  • Explicit modeling of pathogen mutation and individual memory immune responses.
  • Development of a reduced model using a system of difference equations with a generalized immune class.
  • Analysis of model transitions to identify different epidemic behaviors.

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Main Results:

  • Observed four distinct epidemic behaviors: extinction, endemic infection, periodic outbreaks, and outbreaks followed by extinction.
  • Identified parameter ranges for each observed behavior.
  • Demonstrated that rapid pathogen mutation is essential for pathogen viability in highly connected populations.

Conclusions:

  • The relationship between immune memory and pathogen mutation dictates epidemic patterns.
  • Pathogen mutation rate is a critical factor for sustained epidemics, especially in dense populations.