Clustering for epidemics on networks: A geometric approach

Area of Science:

• Epidemiology
• Network Science
• Mathematical Biology

Background:

• Infectious diseases spread through complex contact networks, posing challenges for epidemic control due to their large scale.
• Current clustering methods often rely on restrictive network properties like equitable partitions, limiting their applicability.
• Simplifying epidemic dynamics by analyzing cluster interactions is desirable for managing large-scale outbreaks.

Purpose of the Study:

• To propose a geometric approach for identifying networks where epidemic outbreaks can be simplified to cluster interactions.
• To derive a closed-form solution for Susceptible-Infected-Susceptible (SIS) epidemics on complete graphs using an N-intertwined mean-field approximation.
• To develop low-complexity approximations and bounds for epidemic dynamics on general networks by relaxing equitable partition constraints.

Main Methods:

• A novel geometric framework to characterize networks amenable to cluster-based epidemic analysis.
• Derivation of exact solutions for SIS epidemic models on complete graphs via N-intertwined mean-field approximation.
• Development of approximation techniques for epidemic modeling on arbitrary networks, bypassing equitable partition requirements.

Main Results:

• Identification of specific network structures where epidemic dynamics effectively reduce to inter-cluster interactions.
• Obtained closed-form solutions for SIS epidemics on complete graphs, applicable to various initial conditions.
• Established computationally efficient approximations and bounds for epidemic spread on complex, non-equitably partitioned networks.

Conclusions:

• The proposed geometric approach and relaxed partitioning methods offer a significant advancement in understanding and controlling epidemics on large, complex networks.
• This work provides valuable tools for simplifying epidemic modeling and analysis, moving beyond traditional limitations.
• The findings contribute to the development of more effective strategies for managing infectious disease outbreaks in real-world scenarios.