Disease spread in small-size directed networks: Epidemic threshold, correlation between links to and from nodes, and clustering

JOURNAL OF THEORETICAL BIOLOGY

卷:260

Article

Moslonka-Lefebvre, Mathieu^1,2,3  Pautasso, Marco¹  Jeger, Mike J.¹ 

[1] Univ London Imperial Coll Sci Technol & Med, Div Biol, Ascot SL5 7PY, Berks, England

[2] ENS Cachan, Biochem & Bioengn Dept, F-94230 Cachan, France

[3] Univ Paris 11, Dept Biol, F-91405 Orsay, France

关键词: Commercial transport;    Disease management;    Food webs;    Initial conditions;    Spread of ideas;    Susceptible-infected-susceptible (SIS);   

DOI  :  10.1016/j.jtbi.2009.06.015

来源: Elsevier

【 摘 要 】

Network epidemiology has mainly focused on large-scale complex networks. It is unclear whether findings of these investigations also apply to networks of small size. This knowledge gap is of relevance for many biological applications, including meta-communities, plant-pollinator interactions and the spread of the oomycete pathogen Phytophthora ramorum in networks of plant nurseries. Moreover, many small-size biological networks are inherently asymmetrical and thus cannot be realistically modelled with undirected networks. We modelled disease spread and establishment in directed networks of 100 and 500 nodes at four levels of connectance in six network structures (local, small-world, random, one-way, uncorrelated, and two-way scale-free networks). The model was based on the probability of infection persistence in a node and of infection transmission between connected nodes. Regardless of the size of the network, the epidemic threshold did not depend on the starting node of infection but was negatively related to the correlation coefficient between in- and out-degree for all structures, unless networks were sparsely connected. In this case clustering played a significant role. For small-size-scale free directed networks to have a lower epidemic threshold than other network structures, there needs to be a positive correlation between number of links to and from nodes. When this correlation is negative (one-way scale-free networks), the epidemic threshold for small-size networks can be higher than in non-scale-free networks. Clustering does not necessarily have an influence on the epidemic threshold if connectance is kept constant. Analyses of the influence of the clustering on the epidemic threshold in directed networks can also be spurious if they do not consider simultaneously the effect of the correlation coefficient between in- and out-degree. (C) 2009 Elsevier Ltd. All rights reserved.

【 授权许可】

Free