SIS and SIR Epidemic Models Under Virtual Dispersal

Area of Science:

• Mathematical Biology
• Epidemiology
• Computational Modeling

Background:

• Traditional multi-group epidemic models rely on contact rates, which are difficult to measure in heterogeneous populations.
• Understanding disease dynamics in interconnected populations is crucial for effective public health interventions.

Purpose of the Study:

• To develop a novel multi-group epidemic framework using virtual dispersal, incorporating residence time and local environmental risk.
• To analyze the impact of dispersal behavior on disease dynamics in an n-patch SIS model and a two-patch SIR model.

Main Methods:

• Developed a virtual dispersal framework that replaces traditional contact rates with residence time and local environmental risk.
• Applied the framework to an n-patch SIS model, calculating the basic reproduction number (R0) as a function of the patch residence-time matrix.
• Utilized phenomenological modeling to explore disease-prevalence-driven decisions and their effect on disease dynamics.

Main Results:

• The n-patch SIS model exhibits robust dynamics with a unique, globally stable endemic equilibrium when patches are strongly connected and R0 > 1, and a globally stable disease-free equilibrium when R0 < 1.
• Dispersal behavior, as defined by the residence-time matrix, profoundly influences disease dynamics at the single-patch level, capable of promoting or eliminating endemic disease.
• The framework demonstrated the connection between disease invasion processes and the final epidemic size in a two-patch SIR model.

Conclusions:

• The virtual dispersal framework offers a powerful alternative to traditional methods for modeling epidemics in multi-group settings.
• Residence time and local environmental factors are critical determinants of disease spread and persistence.
• The model highlights the significant impact of dispersal strategies on disease control and management, especially in less connected populations.