Propagation thresholds in a diffusive epidemic model with latency and vaccination

Area of Science:

• Epidemiology
• Mathematical Biology
• Dynamical Systems

Background:

• Understanding disease propagation is crucial for public health interventions.
• Diffusive epidemic models with latency and vaccination are essential for studying disease dynamics.
• Spatial spread and its thresholds require detailed mathematical analysis.

Purpose of the Study:

• To investigate propagation thresholds in a diffusive epidemic model incorporating latency and vaccination.
• To analyze the spatial expansion features of infected populations under specific initial conditions.
• To determine the relationship between minimal spreading speed and traveling wave solutions.

Main Methods:

• Analysis of a diffusive epidemic model with latency and vaccination.
• Study of spatial expansion under exponentially decaying initial conditions.
• Investigation of convergence using compact open topology for finite spreading speeds.
• Characterization of minimal spreading speed via traveling wave solutions.

Main Results:

• Different leftward and rightward spreading speeds were observed based on initial decaying values.
• Convergence was studied for finite spreading speeds.
• The minimal spreading speed was identified as the minimal wave speed of traveling wave solutions.
• Vaccination was shown to decrease the spatial expansion ability of the disease.

Conclusions:

• The study elucidates the spatial dynamics of epidemic propagation in a diffusive model.
• Asymptotic behavior of traveling wave solutions is key to distinguishing minimal spreading speeds.
• Vaccination emerges as a significant factor in mitigating disease spatial spread.