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Epidemic spread dynamics were studied, revealing a novel "front stoppage" phenomenon where infection pulses can decay unexpectedly due to bistable dynamics and transmission rates. This impacts understanding epidemic invasion speeds.

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Area of Science:

  • Epidemiology
  • Mathematical Biology
  • Dynamical Systems

Background:

  • Epidemic spatial spread is often modeled using reaction-diffusion equations.
  • Bistable dynamics can lead to complex phenomena like traveling waves.
  • Understanding invasion dynamics is crucial for public health interventions.

Purpose of the Study:

  • To investigate the spatial spread of an epidemic with bistable dynamics.
  • To analyze the front propagation phenomenon numerically and theoretically.
  • To identify conditions leading to unexpected cessation of epidemic spread.

Main Methods:

  • Numerical simulations of epidemic spread.
  • Theoretical analysis using a four-dimensional phase plane.
  • Comparison of numerical and theoretical results for front profiles and invasion speed.

Main Results:

  • The study found good agreement between numerical and theoretical results for epidemic front profiles and invasion speeds.
  • A novel phenomenon termed "front stoppage" was discovered.
  • In certain parameter regimes, the epidemic front ceases to exist, leading to decay of the infection pulse.

Conclusions:

  • Bistable dynamics can result in the complete stoppage of epidemic spread, even after an initial outbreak.
  • The findings challenge the assumption of continuous invasion in all epidemic models.
  • This research highlights the importance of considering complex dynamics in epidemic modeling.