Abstract
Contact networks provide insights on disease spread due to the duration of close proximity interactions. For systems governed by consensus dynamics, network structure is key to optimising the spread of information. For disease spread over contact networks, the structure would be expected to be similarly influential. However, metrics that are essentially agnostic to the network’s structure, such as weighted degree (strength) centrality and its variants, perform near-optimally in selecting effective spreaders. These degree-based metrics outperform eigenvector centrality, despite disease spread over a network being a random walk process. This paper improves eigenvector-based spreader selection by introducing the non-linear relationship between contact time and the probability of disease transmission into the assessment of network dynamics. This approximation of disease spread dynamics is achieved by altering the Laplacian matrix, which in turn highlights why nodes with a high degree are such influential disease spreaders. From this approach, a trichotomy emerges on the definition of an effective spreader where, for susceptible-infected simulations, eigenvector-based selections can either optimise the initial rate of infection, the average rate of infection, or produce the fastest time to full infection of the network. Simulated and real-world human contact networks are examined, with insights also drawn on the effective adaptation of ant colony contact networks to reduce pathogen spread and protect the queen ant.
Highlights
Despite the commonality of spreading process—such as consensus, disease spread, and rumour propagation—De Arruda et al (2014) notes that the efficacy of centrality measures, in identifying effective spreaders, differs depending on the system dynamics
Visualising spreader selection Algorithm 1 is shown in operation in Fig. 1 for s = 1 and s = 0.1, where it is applied to a hospital ward contact network from Vanhems et al
The system eigenvectors capture the influence of disease spreaders, when the network dynamics are accurately represented
Summary
Despite the commonality of spreading process—such as consensus, disease spread, and rumour propagation—De Arruda et al (2014) notes that the efficacy of centrality measures, in identifying effective spreaders, differs depending on the system dynamics. Given the clear relationship between random walk and spreading processes it is notable that the efficacy of eigenvector-based spreader selection varies with the system dynamics; Clark et al (2019) details the efficacy of eigenvector assessment for consensus dynamics, while De Arruda et al (2014) notes the inferiority of eigenvector centrality for determining the influence of disease spreaders. Degree-based metrics (which include k-shell/k-core strategies) have been repeatedly found to identify a system’s effective spreaders as in De Arruda et al (2014), Kitsak et al (2010), Da Silva et al (2012), Zeng and Zhang (2013), Wang et al (2016), Liu et al (2016), Salamanos et al (2017) and Jiang et al (2019). We aim to highlight that, as with consensus dynamics, a system’s eigenvectors capture the interplay of dynamics and network structure that is fundamental to determining the effectiveness of disease spreaders
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