A novel self-adaptive SIS model based on the mutual interaction between a graph and its line graph

Area of Science:

• Epidemiology
• Network Science
• Complex Systems

Background:

• Standard epidemic models often overlook the intricate dynamics of network structures.
• The interplay between network topology and disease spread is crucial for understanding diffusion processes.

Purpose of the Study:

• To propose a new network-based self-adaptive epidemic model.
• To investigate the influence of network structure and its line graph on epidemic dynamics.
• To introduce a novel eigenvector centrality measure based on network and edge properties.

Main Methods:

• Implementation of a susceptible-infected-susceptible (SIS) model on networks and their line graphs.
• Analysis of existence and stability conditions for endemic and disease-free states.
• Development and application of a new eigenvector centrality metric.
• Numerical simulations on synthetic graphs (cycle, regular, star).

Main Results:

• The proposed model demonstrates real-time re-modulation of graph weights based on infection probabilities.
• The coupling between the graph and its line graph acts as a reinforcement factor for diffusion.
• A new eigenvector centrality is introduced, considering both neighboring nodes and connected edges.
• Numerical simulations validate the model's ability to capture empirical behavioral adoption mechanisms.

Conclusions:

• The network-based self-adaptive epidemic model offers a more realistic approach to studying disease spread.
• The model's adaptive nature and novel centrality measure provide new insights into network dynamics.
• The findings have implications for understanding diffusion and adoption processes in complex systems.