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Understanding the temporal pattern of spreading in heterogeneous networks: Theory of the mean infection time
For a reliable prediction of an epidemic or information spreading pattern in complex systems, well-defined measures are essential. In the susceptible-infected model on heterogeneous networks, the cluster of infected nodes in the intermediate-time regime exhibits too large fluctuation in size to use...
Autores principales: | , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
American Physical Society
2019
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7217551/ https://www.ncbi.nlm.nih.gov/pubmed/30999425 http://dx.doi.org/10.1103/PhysRevE.99.032309 |
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author | Lee, Mi Jin Lee, Deok-Sun |
author_facet | Lee, Mi Jin Lee, Deok-Sun |
author_sort | Lee, Mi Jin |
collection | PubMed |
description | For a reliable prediction of an epidemic or information spreading pattern in complex systems, well-defined measures are essential. In the susceptible-infected model on heterogeneous networks, the cluster of infected nodes in the intermediate-time regime exhibits too large fluctuation in size to use its mean size as a representative value. The cluster size follows quite a broad distribution, which is shown to be derived from the variation of the cluster size with the time when a hub node was first infected. On the contrary, the distribution of the time taken to infect a given number of nodes is well concentrated at its mean, suggesting the mean infection time is a better measure. We show that the mean infection time can be evaluated by using the scaling behaviors of the boundary area of the infected cluster and use it to find a nonexponential but algebraic spreading phase in the intermediate stage on strongly heterogeneous networks. Such slow spreading originates in only small-degree nodes left susceptible, while most hub nodes are already infected in the early exponential-spreading stage. Our results offer a way to detour around large statistical fluctuations and quantify reliably the temporal pattern of spread under structural heterogeneity. |
format | Online Article Text |
id | pubmed-7217551 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2019 |
publisher | American Physical Society |
record_format | MEDLINE/PubMed |
spelling | pubmed-72175512020-05-13 Understanding the temporal pattern of spreading in heterogeneous networks: Theory of the mean infection time Lee, Mi Jin Lee, Deok-Sun Phys Rev E Articles For a reliable prediction of an epidemic or information spreading pattern in complex systems, well-defined measures are essential. In the susceptible-infected model on heterogeneous networks, the cluster of infected nodes in the intermediate-time regime exhibits too large fluctuation in size to use its mean size as a representative value. The cluster size follows quite a broad distribution, which is shown to be derived from the variation of the cluster size with the time when a hub node was first infected. On the contrary, the distribution of the time taken to infect a given number of nodes is well concentrated at its mean, suggesting the mean infection time is a better measure. We show that the mean infection time can be evaluated by using the scaling behaviors of the boundary area of the infected cluster and use it to find a nonexponential but algebraic spreading phase in the intermediate stage on strongly heterogeneous networks. Such slow spreading originates in only small-degree nodes left susceptible, while most hub nodes are already infected in the early exponential-spreading stage. Our results offer a way to detour around large statistical fluctuations and quantify reliably the temporal pattern of spread under structural heterogeneity. American Physical Society 2019-03-29 2019-03 /pmc/articles/PMC7217551/ /pubmed/30999425 http://dx.doi.org/10.1103/PhysRevE.99.032309 Text en ©2019 American Physical Society This article is made available via the PMC Open Access Subset for unrestricted re-use and analyses in any form or by any means with acknowledgement of the original source. |
spellingShingle | Articles Lee, Mi Jin Lee, Deok-Sun Understanding the temporal pattern of spreading in heterogeneous networks: Theory of the mean infection time |
title | Understanding the temporal pattern of spreading in heterogeneous networks: Theory of the mean infection time |
title_full | Understanding the temporal pattern of spreading in heterogeneous networks: Theory of the mean infection time |
title_fullStr | Understanding the temporal pattern of spreading in heterogeneous networks: Theory of the mean infection time |
title_full_unstemmed | Understanding the temporal pattern of spreading in heterogeneous networks: Theory of the mean infection time |
title_short | Understanding the temporal pattern of spreading in heterogeneous networks: Theory of the mean infection time |
title_sort | understanding the temporal pattern of spreading in heterogeneous networks: theory of the mean infection time |
topic | Articles |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7217551/ https://www.ncbi.nlm.nih.gov/pubmed/30999425 http://dx.doi.org/10.1103/PhysRevE.99.032309 |
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