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A simple influenza model with complicated dynamics.

M G Roberts1, R I Hickson2,3, J M McCaw3,4

  • 1Institute of Natural and Mathematical Sciences, New Zealand Institute for Advanced Study and the Infectious Disease Research Centre, Massey University, Private Bag 102 904, North Shore Mail Centre, Auckland, New Zealand. m.g.roberts@massey.ac.nz.

Journal of Mathematical Biology
|August 30, 2018
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Summary
This summary is machine-generated.

Influenza dynamics are unpredictable due to waning immunity and viral drift. Past epidemics do not reliably forecast future influenza seasons, highlighting the complexity of infectious disease modeling.

Keywords:
Discrete dynamicsDynamical systemsSeasonal influenzaTransmission model

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Area of Science:

  • Epidemiology
  • Mathematical Biology
  • Virology

Background:

  • Influenza-like infections exhibit complex dynamics.
  • Understanding these dynamics is crucial for public health interventions.
  • Factors like waning immunity and viral evolution contribute to unpredictability.

Purpose of the Study:

  • To develop and analyze a mathematical model for influenza-like infection dynamics.
  • To investigate the impact of waning immunity and antigenic drift on disease patterns.
  • To explore the potential for complex and chaotic behavior in influenza transmission.

Main Methods:

  • A hybrid mathematical model combining differential equations (within-season) and discrete maps (between-seasons).
  • Analysis of the model's behavior, including fixed points, periodic solutions, and chaotic dynamics.
  • Demonstration of distinct basins of attraction for specific parameter values.

Main Results:

  • The between-season model exhibits diverse dynamics, including stable states, periodic outbreaks, and chaotic patterns.
  • Identified the existence of multiple basins of attraction, where initial conditions dictate long-term outcomes.
  • Demonstrated that influenza dynamics are not inherently regular.

Conclusions:

  • Influenza dynamics are inherently complex and can be highly irregular.
  • Predicting future influenza seasons based on past epidemics is unreliable.
  • The model provides insights into the drivers of influenza variability and unpredictability.