Novel spatial profiles of some diffusive SIS epidemic models

Area of Science:

• Epidemiology
• Mathematical Biology
• Reaction-Diffusion Systems

Background:

• Understanding spatial spread of infectious diseases is crucial for public health interventions.
• Reaction-diffusion models are powerful tools for analyzing epidemic dynamics in heterogeneous environments.
• Previous studies often assumed homogeneous populations or unlimited movement of infected individuals.

Purpose of the Study:

• To investigate the spatial distribution of susceptible and infected populations in SIS epidemic models.
• To analyze the impact of restricted movement of infected individuals on epidemic spread.
• To compare models with constant versus varying total population numbers.

Main Methods:

• Analysis of two SIS epidemic reaction-diffusion models with mass action infection.
• Focus on scenarios with small movement rates for infected individuals.
• Theoretical analysis complemented by numerical simulations.

Main Results:

• In constant population models, susceptible individuals stabilize at the minimum risk level, and infected individuals concentrate at highest-risk locations.
• In varying population models (with births/deaths), susceptible populations may not stabilize to a constant, and infected distribution depends on risk function complexity.
• Infected populations can concentrate at isolated points, aggregate in high-risk intervals, or spread throughout the habitat.

Conclusions:

• The spatial profile of epidemics is highly sensitive to population dynamics and the heterogeneity of the environment's risk landscape.
• Restricted movement of infected individuals can lead to significant spatial aggregation at high-risk zones.
• The interplay between population dynamics and environmental risk dictates the ultimate spatial spread of infectious diseases.