the threshold is not expressed in terms of the absolute number of a node’s neighbors choosing a given alternative, but the corresponding fraction of the neighborhood. This is a natural condition to impose for decision making problems, because the more signals a decision maker receives, the less significant any one signal becomes. (iii)

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

assortative and scale-free networks with power exponent more than 3 will have an epidemic threshold. also as the clustering increases, so does the epidemic threshold. so random and scale free networks with exponent less than 3 make it very easy to propagade desease and information. Aiello et al (2000) showed that giant component appears in networks with power-law distributions less than 3.47 which may mean that the existence of a giant component in the network makes it easier for information to propagate. That's why random networks with the sufficient number of connections and disassortative networks as well as scale-free networks with distribution less than 3 propagate information very easily.