We investigate the sensitivity of epidemic behavior to a bounded
susceptibility constraint -- susceptible nodes are infected by their neighbors
via the regular SI/SIS dynamics, but subject to a cap on the infection rate.
Such a constraint is motivated by modern social networks, wherein messages are
broadcast to all neighbors, but attention spans are limited. Bounded
susceptibility also arises in distributed computing applications with download
bandwidth constraints, and in human epidemics under quarantine policies.
Network epidemics have been extensively studied in literature; prior work
characterizes the graph structures required to ensure fast spreading under the
SI dynamics, and long lifetime under the SIS dynamics. In particular, these
conditions turn out to be meaningful for two classes of networks of practical
relevance -- dense, uniform (i.e., clique-like) graphs, and sparse, structured
(i.e., star-like) graphs. We show that bounded susceptibility has a surprising
impact on epidemic behavior in these graph families. For the SI dynamics,
bounded susceptibility has no effect on star-like networks, but dramatically
alters the spreading time in clique-like networks. In contrast, for the SIS
dynamics, clique-like networks are unaffected, but star-like networks exhibit a
sharp change in extinction times under bounded susceptibility.
Our findings are useful for the design of disease-resistant networks and
infrastructure networks. More generally, they show that results for existing
epidemic models are sensitive to modeling assumptions in non-intuitive ways,
and suggest caution in directly using these as guidelines for real systems