Ring vaccination strategy in networks: A mixed percolation approach

Area of Science:

• Epidemiology
• Network Science
• Mathematical Modeling

Background:

• Ring vaccination aims to control disease outbreaks by immunizing contacts of infected individuals.
• Previous models linked ring vaccination to link percolation, primarily in complex networks.
• A comprehensive understanding across network types is needed.

Purpose of the Study:

• To extend the susceptible-infected-recovered (SIR) epidemic model with ring vaccination to complex and spatial networks.
• To propose and validate a mixed percolation (links and nodes) framework for this model.
• To map epidemic dynamics to percolation processes and identify epidemic-free regions.

Main Methods:

• Developed an extended SIR epidemic model incorporating ring vaccination.
• Applied a mixed percolation (links and nodes) framework to analyze the model.
• Investigated network structures including complex networks and spatial networks (Waxman model).
• Determined epidemic-free regions using phase diagrams based on network and epidemic parameters.

Main Results:

• The SIR model with ring vaccination is equivalent to a mixed percolation process in both complex and spatial networks.
• A phase diagram illustrates epidemic-free regions based on wiring cost and epidemic parameters.
• For long recovery times, the model maps to pure node percolation, unlike the SIR model without ring vaccination (link percolation).

Conclusions:

• The mixed percolation framework offers a more complete description of ring vaccination dynamics than prior link percolation models.
• This approach is applicable to diverse network structures, including spatial networks.
• Understanding the mapping to percolation processes aids in predicting and controlling epidemic spread.