Contagion spreading on complex networks with local deterministic dynamics

• We model spreading of contagions using fitness-based local deterministic dynamics.
• Contagion-dependent stationary state is followed by initial exponential growth.
• For certain dynamical rule, high prevalence without the activity of hubs is seen.
• “Moving under the radar” is severely hindered in heterogeneous populations.
• Small-world effect is shown to be the key feature of topology.

Typically, contagion strength is modeled by a transmission rate λλ, 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, 0⩽α⩽10⩽α⩽1, 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 quality-dependent 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.