A spatial SIS model in heterogeneous environments with vary advective rate

Area of Science:

• Epidemiology
• Mathematical Biology
• Spatial Dynamics

Background:

• The spread of infectious diseases is often influenced by environmental factors and movement patterns.
• Spatial modeling is crucial for understanding disease dynamics in heterogeneous landscapes.

Purpose of the Study:

• To investigate a spatial Susceptible-Infected-Susceptible (SIS) model in heterogeneous environments.
• To analyze the impact of varying advective rates on disease persistence and stability.
• To determine the conditions for disease eradication versus endemicity.

Main Methods:

• Mathematical modeling using a spatial SIS framework.
• Analysis of equilibrium points: disease-free equilibrium (DFE) and endemic equilibrium.
• Asymptotic stability analysis based on the basic reproduction number ($ \mathcal{R}_0 $).
• Investigation of the influence of diffusion on DFE stability.

Main Results:

• The unique disease-free equilibrium (DFE) is asymptotically stable when $ \mathcal{R}_0 < 1 $.
• The existence of an endemic equilibrium is established when $ \mathcal{R}_0 > 1 $.
• Diffusion significantly affects the stability of the DFE.

Conclusions:

• The basic reproduction number ($ \mathcal{R}_0 $) is a critical threshold for disease persistence in this spatial SIS model.
• Environmental heterogeneity and advection play a significant role in disease dynamics.
• Understanding these spatial dynamics is essential for effective disease control strategies.