hypothesis: random networks have much more epidemic capacity in that it can spread globally much easier (given that the infection rate is above a threshold and that the degree is not too high to prevent the spread through clustering or lowered threshold in SIRS model). also, the more randomized the network is, the more short-lived and periodical the epidemic spread is.
on the other hand, scale-free structure is different in the sense that the latter has less capacity for global epidemics, but higher capacity for endemic state of epidemics. generally, to spread something virally through the network, the best structure is randomized scale-free structure, which allows for local endemic states and consistent sustainment of a certain epidemics level, while at the same time, temporary randomization allows for informational cascades to occur. however, this randomization is only temporary to avoid too much interconnectedness.

random graphswith power law degree distributions tend to be much less vulnerable to random shocks than uniform random graphs with the same z, a point observed else- where (19, 20) with respect to network connectivity. Although this distinction between threshold and network heterogeneity is slightly surprising (because both kinds of heterogeneity are related by the fractional threshold condition), it is understandable. Nodes that are vulnerable because of a low threshold can still be well connected to the network, making them ideal early adopters. But nodes that are vulnerable to small perturbations because they have very few neighbors are therefore also poorly connected; hence, they have difficulty propagating any influence.

Epidemic threshold is higher in random networks than in scale free networks only if superconnected nodes have higher number of in/out links.



(Pautasso, Jeger, 2007 Epidemic threshold and network structure)



On the other extreme, highly disordered networks, with

p . 0.5, exhibit a low average clusterization and also a

low dispersion around it. There is an intermediate range

of p, between 0.1 and 0.5, where the average clusterization

shifts from high to low, but the distributions are wide.

This indicates that, in this range, the system is a mixture of highly ordered, highly clustered regions and random, lowly clustered ones. If we consider that the clustering structure determines a partition of the whole system into smaller, interacting, subsystems, the global behavior of the system

could be interpreted as a superposition of the subsystems’ dynamics. When p is small, the existence of large clusters (essentially one-dimensional in our model) inhibits the oscillatory

behavior because, once the infection breaks into

such a region, it remains restricted to it a long time until

all the individuals have completed the cycle, orderly and deterministically. As p increases, the number of big, ordered regions decreases. Elements within small regions

with some long range links go through the infection cycle

and become infected again before long.

Kuperman, Abramson, 2000
Small World Effect in an Epidemiological Model