The SIS model with diffusion of virus in the environment

Area of Science:

• Epidemiology
• Mathematical Biology
• Infectious Disease Dynamics

Background:

• Hospital-acquired infections pose significant public health challenges.
• Understanding disease transmission, including direct and indirect routes, is crucial for control.
• Reaction-diffusion models offer a framework to study spatially explicit disease dynamics.

Purpose of the Study:

• To propose and analyze an SIS-type reaction-diffusion model for hospital infections.
• To establish the basic reproduction number (R₀) as a threshold for disease persistence.
• To investigate the existence and properties of traveling wave solutions.

Main Methods:

• Development of an SIS-type reaction-diffusion model incorporating direct and indirect transmission.
• Mathematical analysis to determine the global stability of the disease-free equilibrium based on R₀.
• Application of the geometric singular perturbation method to analyze traveling wave solutions in spatially homogeneous systems.

Main Results:

• The basic reproduction number (R₀) effectively predicts disease-free equilibrium stability (R₀<1 implies stability).
• A critical wave speed exists for traveling wave solutions in spatially homogeneous systems.
• Spatial transmission increases infections, while high pathogen diffusion decreases them in heterogeneous environments.

Conclusions:

• The proposed model provides insights into the complex dynamics of hospital infections.
• R₀ serves as a critical threshold for disease eradication or persistence.
• Spatial factors, including transmission and diffusion, significantly influence infection outcomes.