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Antigenic waves of virus-immune coevolution.

Jacopo Marchi1, Michael Lässig2, Aleksandra M Walczak3

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Pathogen evolution, like influenza, is driven by host immune pressure. This study models viral-immune coevolution, revealing an

Keywords:
coevolutionfitness wavehost–pathogen dynamicsviral evolution

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Area of Science:

  • Evolutionary biology
  • Epidemiology
  • Mathematical modeling

Background:

  • Pathogen evolution, including viruses like influenza, is shaped by host immune system pressure.
  • Host immune systems adapt to circulating pathogens, creating a dynamic coevolutionary arms race.
  • Understanding these dynamics is crucial for forecasting pathogen adaptation and disease spread.

Purpose of the Study:

  • To develop a mathematical theory for host-pathogen coevolution in a finite antigenic space.
  • To analyze the emergence and characteristics of antigenic waves driven by cross-reactivity.
  • To investigate the emergent timescales in viral-immune coevolution and their relation to influenza dynamics.

Main Methods:

  • Mathematical modeling of coevolutionary dynamics.
  • Analysis of viral and immune system interactions in a finite-dimensional antigenic space.
  • Derivation of analytical results for antigenic wave properties and persistence times.

Main Results:

  • Demonstrated the emergence of an antigenic wave, influenced by cross-reactivity.
  • Provided analytical results for the wave's shape, speed, and diffusion.
  • Identified an emergent timescale (persistence time) longer than viral population coalescence time.
  • Linked coevolutionary dynamics to observed antigenic turnover in influenza.

Conclusions:

  • The developed mathematical framework offers a tractable model for pathogen-host coevolution.
  • Cross-reactivity plays a key role in shaping antigenic waves and evolutionary predictability.
  • Emergent timescales in coevolution can exceed those of simple viral population dynamics.