Epidemic Extinction and Control in Heterogeneous Networks

Area of Science:

• Epidemiology
• Network Science
• Mathematical Biology

Background:

• Understanding epidemic extinction in finite networks is crucial for public health interventions.
• Network topology significantly influences disease dynamics and extinction probabilities.

Purpose of the Study:

• To generalize large fluctuation theory to predict optimal epidemic extinction paths in random networks.
• To identify extinction patterns in heterogeneous networks and develop optimal control strategies.

Main Methods:

• Applied large fluctuation theory to random networks with specified degree distributions.
• Analyzed extinction dynamics in various network configurations, including truncated power laws.
• Developed optimal control strategies based on network topology and finite-size fluctuations.

Main Results:

• Predicted a limiting extinction path for heterogeneous networks: initial decrease in low-degree nodes, followed by rapid extinction in high-degree nodes, and residual low-degree extinction.
• Demonstrated that finite-size fluctuations depend on network topology.
• Identified an optimal control strategy involving treatment of both high- and low-degree nodes.

Conclusions:

• The developed theory accurately predicts epidemic extinction paths in diverse network structures.
• Optimal control strategies informed by network topology and dynamical fluctuations are more effective.
• Targeted interventions on both high- and low-degree nodes are recommended for efficient epidemic control.