Metastable localization of diseases in complex networks.

Area of Science:

• Epidemiology
• Network Science
• Mathematical Modeling

Background:

• Understanding epidemic spread on complex networks is crucial.
• Heterogeneous networks with hubs significantly influence disease dynamics.

Purpose of the Study:

• To investigate epidemic localization in susceptible-infective-susceptible (SIS) models on heterogeneous networks.
• To characterize the behavior of localized outbreaks below the epidemic threshold.

Main Methods:

• Analysis of the SIS model on highly heterogeneous networks.
• Study of metastable states and their longevity.
• Examination of the crossover from localized to delocalized states.
• Utilizing random regular graphs with hubs for analysis.

Main Results:

• Localized epidemic states below the threshold are metastable.
• A sharp localization transition is absent; a smooth crossover occurs.
• The distribution of infective nodes can detect these localized outbreaks.

Conclusions:

• Hubs act as centers for epidemic localization in heterogeneous networks.
• Metastable localized outbreaks exhibit a smooth transition rather than a sharp one.
• Network structure and node properties influence epidemic localization and detection.