Spatial correlations in susceptible-infected-susceptible processes on random regular graphs

Area of Science:

• Epidemiology
• Network Science
• Mathematical Biology

Background:

• Network-based susceptible-infected-susceptible (SIS) models are crucial for understanding infectious disease transmission.
• Standard models like mean-field and pairwise approximations fail to capture essential spatial correlations in networks, leading to inaccurate predictions.
• Accurate forecasting requires approximations that account for higher-order spatial correlations.

Purpose of the Study:

• To develop a generalized framework for correcting mean-field theory on random regular graphs.
• To derive and simulate a hierarchical system of ordinary differential equations for spatial correlation functions.
• To accurately predict time-dependent global infection density in SIS models on networks.

Main Methods:

• Extension of existing mean-field corrections from regular lattices to random regular graph topologies.
• Derivation of a hierarchical system of ordinary differential equations to model spatial correlation evolution.
• Numerical simulation of the derived equations and comparison with infection dynamics on random networks.

Main Results:

• The developed framework successfully predicts time-dependent global infection density.
• The model shows good agreement with numerical simulations of SIS processes on random networks.
• The results significantly improve upon existing corrections to mean-field theory for SIS models.

Conclusions:

• Structural randomness in networks plays a critical role in the dynamical trajectories of infectious diseases.
• The new framework provides an in-depth characterization of disease dynamics considering network structure.
• This work offers a more accurate and analytically tractable approach for infectious disease forecasting on complex networks.