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Abstract
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Typically, contagion strength is modeled by a transmission rate k, whereby all nodes in a
network are treated uniformly in a mean-field approximation. However, local agents react
differently to the same contagion based on their local characteristics. Following our recent
work (Montakhab and Manshour, 2012 [42]), we investigate contagion spreading models
with local dynamics on complex networks. We therefore quantify contagions by their quality,
, and follow their spreading as their transmission condition (fitness) is evaluated
by local agents. Instead of considering stochastic dynamics, here we consider
various deterministic local rules. We find that initial spreading with exponential qualitydependent
time scales is followed by a stationary state with a prevalence depending on
the quality of the contagion. We also observe various interesting phenomena, for example,
high prevalence without the participation of the hubs. This special feature of our ‘‘threshold
rule’’ provides a mechanism for high prevalence spreading without the participation of
‘‘super-spreaders’’, in sharp contrast with many standard mechanism of spreading where
hubs are believed to play the central role. On the other hand, if local nodes act as agents
who stop the transmission once a threshold is reached, we find that spreading is severely
hindered in a heterogeneous population while in a homogeneous one significant spreading
may occur. We further decouple local characteristics from underlying topology in order to
study the role of network topology in various models and find that as long as small-world
effect exists, the underlying topology does not contribute to the final stationary state but
only affects the initial spreading velocity.
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