Influence of the network topology on epidemic spreading

Abstract

The influence of the network's structure on the dynamics of spreading processes has been extensively studied in the last decade. Important results that partially answer this question show a weak connection between the macroscopic behavior of these processes and specific structural properties in the network, such as the largest eigenvalue of a topology related matrix. However, little is known about the direct influence of the network topology on the microscopic level, such as the influence of the (neighboring) network on the probability of a particular node's infection. To answer this question, we derive both an upper and a lower bound for the probability that a particular node is infective in a susceptible-infective-susceptible model for two cases of spreading processes: reactive and contact processes. The bounds are derived by considering the n-hop neighborhood of the node; the bounds are tighter as one uses a larger n-hop neighborhood to calculate them. Consequently, using local information for different neighborhood sizes, we assess the extent to which the topology influences the spreading process, thus providing also a strong macroscopic connection between the former and the latter. Our findings are complemented by numerical results for a real-world email network. A very good estimate for the infection density ρ is obtained using only two-hop neighborhoods, which account for 0.4% of the entire network topology on average.

Interactions between tick and transmitted pathogens evolved to minimise competition through nested and coherent networks

“…We calculated 24 the Node Betweenness Centrality (NBC) and the PageRank (PR) of each node as measures of the importance of these taxa in the network. In parasitic networks, host NBC is related to the number of parasites infecting a host 24 and to the parasite’s host range and transmission ability at the level of the entire network 25 . The PR assigns a universal rank to nodes based on the importance of the other nodes to which it is linked.…”

Centrality in primate–parasite networks reveals the potential for the transmission of emerging infectious diseases to humans

“…Infection dynamics have been investigated extensively using social networks in which nodes represent individuals that are connected through social or sexual contacts (8,9). Ecological networks involve similar connections among species (rather than individuals) and have been used to investigate a wide range of important questions involving food webs, mutualisms, and antagonistic interactions (10).…”

Modeling Information Spreading on Complex Networks

“…One can apply the methodology of [29] to obtain better bounds on the probabilities of infection for the case when the degree of the nodes is not very high for the aforementioned approximations to hold. Comparing the model predictions to real data is a key question to its usefulness.…”

“…The cases when only one information type has transmission to forgetting ratio above the threshold reduce to a SIS epidemic model, and for this model the question of determining bounds on the fixed point has been solved [29].…”