Continual Versus Occasional Spreading In Networks: Modeling Spreading Thresholds In Epidemic Processes

Epidemic processes are widely used as an abstraction for various real-world phenomena - human infections, computer viruses, rumors, information broadcasts, etc. [5, 1, 3]. Under the SIR model (susceptible-infected-removed/recovered) in finite networks, the effective reproduction number, R(), decreases as nodes become infected and removed. Hence, the spread process remains active for a while but eventually dies out (following R < 1, "herd-immunity"). Such threshold phenomena have been observed empirically. In these special days of COVID-19, estimations of the spreadinduced Herd Immunity Threshold (HIT) are a key factor in directing strategic decisions concerning the fight against the pandemic.