From epidemic hotspots to super-spreading events

We examine the phenomenon of localization and super-spreading by introducing
a \emph{superhub} of degree $q\sim N^\alpha$ on different network
topologies with $N$ nodes.
It provides high heterogeneous and controlled environments
by tuning the gap exponent $\alpha$.
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Recently, localization phenomenon attracted much attention
to the issue of epidemic spreading on networks, where this phenomenon means
persistence of an island of disease below the epidemic threshold around a
strongly connected node or a dense cluster.
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This phenomenon hinders the observation of the epidemic threshold in
complex networks with hubs and heavy-tailed degree distributions. The
problem is that the SIS (susceptible-infective-susceptible) epidemic model
has an absorbing state in which infection is absent, and so below the
epidemic threshold, islands of disease with a finite number of infective
nodes cannot survive forever. In other words, a system with a finite
number of infected nodes has a non-zero probability to recover
immediately.
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For a large but finite number of infected nodes, however, this probability
is small, so the complete recovery can take a long time. We show that
in the heterogeneous SIS model localization should be only metastable,
manifesting itself in the form of long-lasting local outbreaks of the
disease below the epidemic threshold.
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Moreover, super-spreading events in which one or a few infective individuals
spread a disease providing an unusually large number of second cases, has
great importance on current understanding on epidemic spreading.
central issue is that heterogeneity in population structures, such as the
presence of outliers on networked systems, accelerates infectious disease
spread.
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We present under what circumstances the role reversal from
a hotspot to a super-spreading event takes over for the SIS model
on heterogeneous networks.

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\emph{RSF would like to thank} FAPEMIG.
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