Outbreaks in susceptible-infected-removed epidemics with multiple seeds

Area of Science:

• Epidemiology
• Network Science
• Mathematical Modeling

Background:

• The susceptible-infected-removed (SIR) model is a fundamental tool for studying infectious disease dynamics.
• Research has primarily focused on epidemic thresholds with infinitesimal initial seeds, leaving finite seed scenarios less explored.
• Network structure significantly influences epidemic spread and phase transitions.

Purpose of the Study:

• To investigate the phase transitions of the SIR model with multiple finite seeds on regular random graphs.
• To clarify the behavior of epidemic models when initiated from a substantial fraction of seeds.
• To analyze the interplay between multiple seeds and epidemic cluster percolation.

Main Methods:

• Utilizing a susceptible-infected-removed (SIR) model framework.
• Employing regular random graphs to represent network structures.
• Deriving percolation transition points for the multi-seed SIR model.
• Analyzing epidemic cluster formation and percolation dynamics.

Main Results:

• The SIR model on networks exhibits two distinct percolation transitions.
• Epidemic clusters originating from multiple seeds percolate at lower infection rates than previously established thresholds for single-seed global outbreaks.
• The presence of multiple seeds alters the conditions under which a global epidemic can emerge.

Conclusions:

• Multiple finite seeds lead to earlier percolation of epidemic clusters compared to single infinitesimal seeds.
• Understanding multi-seed dynamics is crucial for accurate epidemic forecasting in real-world networks.
• This research highlights the importance of initial seeding conditions in network epidemic models.