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How immune dynamics shape multi-season epidemics: a continuous-discrete model in one dimensional antigenic space.

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Mathematical modeling of influenza-like infections reveals that host immunity dynamics significantly impact epidemic predictability. Waning immunity based on time since last infection can lead to complex, unpredictable epidemiological patterns.

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Area of Science:

  • Epidemiology
  • Mathematical Biology
  • Virology

Background:

  • Influenza-like infections pose a significant public health challenge.
  • Understanding the dynamics of infectious diseases is crucial for effective control strategies.
  • Previous models have explored influenza transmission but require further refinement regarding immunity and viral evolution.

Purpose of the Study:

  • To extend a mathematical model for influenza-like infection dynamics.
  • To investigate the impact of waning acquired immunity and antigenic drift on disease patterns.
  • To analyze long-term behaviors under different immunity scenarios.

Main Methods:

  • Utilized a previously published mathematical model.
  • Incorporated waning immunity and punctuated antigenic drift.
  • Employed coupled integral equations within seasons and discrete maps between seasons.
  • Examined scenarios where immunity depends on time since last infection or number of infections.

Main Results:

  • Immunity waning based on time since last infection led to complex dynamics and multiple attractors.
  • Immunity based on the number of infections resulted in a stable fixed point with predictable seasonal epidemics.
  • Combining both immunity paradigms predominantly yielded stable fixed points or periodic solutions.
  • Stochastic perturbations did not fundamentally alter the model's qualitative dynamics.

Conclusions:

  • Host immunity duration significantly influences the predictability of influenza-like epidemics.
  • Time-dependent waning immunity can introduce complex and potentially unpredictable epidemiological dynamics.
  • Mathematical modeling provides valuable insights into the interplay of immunity, viral drift, and disease transmission patterns.