Spatial spread of epidemic with Allee effect.

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.