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Heterogeneous Recovery Rates against SIS Epidemics in Directed Networks
The nodes in communication networks are possibly and most likely equipped
with different recovery resources, which allow them to recover from a virus
with different rates. In this paper, we aim to understand know how to allocate
the limited recovery resources to efficiently prevent the spreading of
epidemics. We study the susceptible-infected-susceptible (SIS) epidemic model
on directed scale-free networks. In the classic SIS model, a susceptible node
can be infected by an infected neighbor with the infection rate and an
infected node can be recovered to be susceptible again with the recovery rate
. In the steady state a fraction of nodes are infected,
which shows how severely the network is infected. We propose to allocate the
recovery rate for node according to its indegree and
outdegree-,
given the finite average recovery rate representing the
limited recovery resources over the whole network. We find that, by tuning the
two scaling exponents and , we can always reduce
the infection fraction thus reducing the extent of infections,
comparing to the homogeneous recovery rates allocation. Moreover, we can find
our optimal strategy via the optimal choice of the exponent and
. Our optimal strategy indicates that when the recovery resources
are sufficient, more resources should be allocated to the nodes with a larger
indegree or outdegree, but when the recovery resource is very limited, only the
nodes with a larger outdegree should be equipped with more resources. We also
find that our optimal strategy works better when the recovery resources are
sufficient but not yet able to make the epidemic die out, and when the indegree
outdegree correlation is small.Comment: 6 figures, conferenc