Evolution of scaling emergence in large-scale spatial epidemic spreading
Zipf's law and Heaps' law are two representatives of the scaling concepts, which play a significant role in the study of complexity science. The coexistence of the Zipf's law and the Heaps' law motivates different understandings on the dependence between these two scalings, which...
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| Veröffentlicht in: | PloS one 2011-07, Vol.6 (7), p.e21197-e21197 |
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| creator | Wang, Lin Li, Xiang Zhang, Yi-Qing Zhang, Yan Zhang, Kan |
| description | Zipf's law and Heaps' law are two representatives of the scaling concepts, which play a significant role in the study of complexity science. The coexistence of the Zipf's law and the Heaps' law motivates different understandings on the dependence between these two scalings, which has still hardly been clarified.
In this article, we observe an evolution process of the scalings: the Zipf's law and the Heaps' law are naturally shaped to coexist at the initial time, while the crossover comes with the emergence of their inconsistency at the larger time before reaching a stable state, where the Heaps' law still exists with the disappearance of strict Zipf's law. Such findings are illustrated with a scenario of large-scale spatial epidemic spreading, and the empirical results of pandemic disease support a universal analysis of the relation between the two laws regardless of the biological details of disease. Employing the United States domestic air transportation and demographic data to construct a metapopulation model for simulating the pandemic spread at the U.S. country level, we uncover that the broad heterogeneity of the infrastructure plays a key role in the evolution of scaling emergence.
The analyses of large-scale spatial epidemic spreading help understand the temporal evolution of scalings, indicating the coexistence of the Zipf's law and the Heaps' law depends on the collective dynamics of epidemic processes, and the heterogeneity of epidemic spread indicates the significance of performing targeted containment strategies at the early time of a pandemic disease. |
| doi_str_mv | 10.1371/journal.pone.0021197 |
| format | Article |
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In this article, we observe an evolution process of the scalings: the Zipf's law and the Heaps' law are naturally shaped to coexist at the initial time, while the crossover comes with the emergence of their inconsistency at the larger time before reaching a stable state, where the Heaps' law still exists with the disappearance of strict Zipf's law. Such findings are illustrated with a scenario of large-scale spatial epidemic spreading, and the empirical results of pandemic disease support a universal analysis of the relation between the two laws regardless of the biological details of disease. Employing the United States domestic air transportation and demographic data to construct a metapopulation model for simulating the pandemic spread at the U.S. country level, we uncover that the broad heterogeneity of the infrastructure plays a key role in the evolution of scaling emergence.
The analyses of large-scale spatial epidemic spreading help understand the temporal evolution of scalings, indicating the coexistence of the Zipf's law and the Heaps' law depends on the collective dynamics of epidemic processes, and the heterogeneity of epidemic spread indicates the significance of performing targeted containment strategies at the early time of a pandemic disease.</description><identifier>ISSN: 1932-6203</identifier><identifier>EISSN: 1932-6203</identifier><identifier>DOI: 10.1371/journal.pone.0021197</identifier><identifier>PMID: 21747932</identifier><language>eng</language><publisher>United States: Public Library of Science</publisher><subject>Air transportation ; Air travel ; Analysis ; Biology ; Coexistence ; Computer simulation ; Containment ; Demographics ; Demography ; Disease control ; Emergence ; Empirical analysis ; Engineering ; Epidemics ; Evolution ; Evolution (Biology) ; Gene expression ; Heterogeneity ; Humans ; Influenza ; Influenza A Virus, H1N1 Subtype - pathogenicity ; Influenza, Human - epidemiology ; Influenza, Human - transmission ; Laws, regulations and rules ; Maximum likelihood method ; Medical laboratories ; Medicine ; Metapopulations ; Models, Theoretical ; Normal distribution ; Pandemics ; Physics ; Scaling ; Spatial analysis ; Spreading ; Time Factors ; Transportation ; Viral infections ; Web applications ; Zipf's Law</subject><ispartof>PloS one, 2011-07, Vol.6 (7), p.e21197-e21197</ispartof><rights>COPYRIGHT 2011 Public Library of Science</rights><rights>2011 Wang et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License: https://creativecommons.org/licenses/by/4.0/ (the “License”), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><rights>Wang et al. 2011</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c757t-9e61c61684359aa52eb4125c8872f6177cce39223b54909272b42f1ec61876933</citedby><cites>FETCH-LOGICAL-c757t-9e61c61684359aa52eb4125c8872f6177cce39223b54909272b42f1ec61876933</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC3128583/pdf/$$EPDF$$P50$$Gpubmedcentral$$Hfree_for_read</linktopdf><linktohtml>$$Uhttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC3128583/$$EHTML$$P50$$Gpubmedcentral$$Hfree_for_read</linktohtml><link.rule.ids>230,314,727,780,784,864,885,2100,2919,23857,27915,27916,53782,53784,79361,79362</link.rule.ids><backlink>$$Uhttps://www.ncbi.nlm.nih.gov/pubmed/21747932$$D View this record in MEDLINE/PubMed$$Hfree_for_read</backlink></links><search><contributor>Montoya, Alejandro Raul Hernandez</contributor><creatorcontrib>Wang, Lin</creatorcontrib><creatorcontrib>Li, Xiang</creatorcontrib><creatorcontrib>Zhang, Yi-Qing</creatorcontrib><creatorcontrib>Zhang, Yan</creatorcontrib><creatorcontrib>Zhang, Kan</creatorcontrib><title>Evolution of scaling emergence in large-scale spatial epidemic spreading</title><title>PloS one</title><addtitle>PLoS One</addtitle><description>Zipf's law and Heaps' law are two representatives of the scaling concepts, which play a significant role in the study of complexity science. The coexistence of the Zipf's law and the Heaps' law motivates different understandings on the dependence between these two scalings, which has still hardly been clarified.
In this article, we observe an evolution process of the scalings: the Zipf's law and the Heaps' law are naturally shaped to coexist at the initial time, while the crossover comes with the emergence of their inconsistency at the larger time before reaching a stable state, where the Heaps' law still exists with the disappearance of strict Zipf's law. Such findings are illustrated with a scenario of large-scale spatial epidemic spreading, and the empirical results of pandemic disease support a universal analysis of the relation between the two laws regardless of the biological details of disease. Employing the United States domestic air transportation and demographic data to construct a metapopulation model for simulating the pandemic spread at the U.S. country level, we uncover that the broad heterogeneity of the infrastructure plays a key role in the evolution of scaling emergence.
The analyses of large-scale spatial epidemic spreading help understand the temporal evolution of scalings, indicating the coexistence of the Zipf's law and the Heaps' law depends on the collective dynamics of epidemic processes, and the heterogeneity of epidemic spread indicates the significance of performing targeted containment strategies at the early time of a pandemic disease.</description><subject>Air transportation</subject><subject>Air travel</subject><subject>Analysis</subject><subject>Biology</subject><subject>Coexistence</subject><subject>Computer simulation</subject><subject>Containment</subject><subject>Demographics</subject><subject>Demography</subject><subject>Disease control</subject><subject>Emergence</subject><subject>Empirical analysis</subject><subject>Engineering</subject><subject>Epidemics</subject><subject>Evolution</subject><subject>Evolution (Biology)</subject><subject>Gene expression</subject><subject>Heterogeneity</subject><subject>Humans</subject><subject>Influenza</subject><subject>Influenza A Virus, H1N1 Subtype - 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Academic</collection><collection>PubMed Central (Full Participant titles)</collection><collection>DOAJ Directory of Open Access Journals</collection><jtitle>PloS one</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Wang, Lin</au><au>Li, Xiang</au><au>Zhang, Yi-Qing</au><au>Zhang, Yan</au><au>Zhang, Kan</au><au>Montoya, Alejandro Raul Hernandez</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Evolution of scaling emergence in large-scale spatial epidemic spreading</atitle><jtitle>PloS one</jtitle><addtitle>PLoS One</addtitle><date>2011-07-01</date><risdate>2011</risdate><volume>6</volume><issue>7</issue><spage>e21197</spage><epage>e21197</epage><pages>e21197-e21197</pages><issn>1932-6203</issn><eissn>1932-6203</eissn><abstract>Zipf's law and Heaps' law are two representatives of the scaling concepts, which play a significant role in the study of complexity science. The coexistence of the Zipf's law and the Heaps' law motivates different understandings on the dependence between these two scalings, which has still hardly been clarified.
In this article, we observe an evolution process of the scalings: the Zipf's law and the Heaps' law are naturally shaped to coexist at the initial time, while the crossover comes with the emergence of their inconsistency at the larger time before reaching a stable state, where the Heaps' law still exists with the disappearance of strict Zipf's law. Such findings are illustrated with a scenario of large-scale spatial epidemic spreading, and the empirical results of pandemic disease support a universal analysis of the relation between the two laws regardless of the biological details of disease. Employing the United States domestic air transportation and demographic data to construct a metapopulation model for simulating the pandemic spread at the U.S. country level, we uncover that the broad heterogeneity of the infrastructure plays a key role in the evolution of scaling emergence.
The analyses of large-scale spatial epidemic spreading help understand the temporal evolution of scalings, indicating the coexistence of the Zipf's law and the Heaps' law depends on the collective dynamics of epidemic processes, and the heterogeneity of epidemic spread indicates the significance of performing targeted containment strategies at the early time of a pandemic disease.</abstract><cop>United States</cop><pub>Public Library of Science</pub><pmid>21747932</pmid><doi>10.1371/journal.pone.0021197</doi><tpages>e21197</tpages><oa>free_for_read</oa></addata></record> |
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| subjects | Air transportation Air travel Analysis Biology Coexistence Computer simulation Containment Demographics Demography Disease control Emergence Empirical analysis Engineering Epidemics Evolution Evolution (Biology) Gene expression Heterogeneity Humans Influenza Influenza A Virus, H1N1 Subtype - pathogenicity Influenza, Human - epidemiology Influenza, Human - transmission Laws, regulations and rules Maximum likelihood method Medical laboratories Medicine Metapopulations Models, Theoretical Normal distribution Pandemics Physics Scaling Spatial analysis Spreading Time Factors Transportation Viral infections Web applications Zipf's Law |
| title | Evolution of scaling emergence in large-scale spatial epidemic spreading |
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