Recursive contact tracing in Reed-Frost epidemic models

Area of Science:

• Epidemiology
• Network Science
• Mathematical Modeling

Background:

• Previous work established a branching-process model for epidemic spread.
• Existing models often simplify population structures and transmission dynamics.

Purpose of the Study:

• To generalize the epidemic model to finite populations and complex contact networks.
• To investigate the impact of recursive contact tracing on epidemic containment.
• To analyze phase transitions in epidemic spread.

Main Methods:

• Developed a Reed-Frost epidemic model with recursive contact tracing and asymptomatic transmission.
• Simulated the model on complete graphs and square lattices.
• Analyzed finite-size scaling of phase transitions.

Main Results:

• Observed a contact-tracing phase transition from epidemic to immune phases with increased network coverage.
• Demonstrated that phase transition scaling aligns with percolation universality classes.
• Quantified the efficacy of recursive contact tracing in uncontained epidemic scenarios.

Conclusions:

• Recursive contact tracing can induce a phase transition to an immune state in finite populations.
• The model provides a framework for understanding epidemic dynamics on general contact networks.
• Contact tracing efficacy is dependent on network coverage and structure.