On analytical approaches to epidemics on networks
One way to describe the spread of an infection on a network is by approximating the network by a random graph. However, the usual way of constructing a random graph does not give any control over the number of triangles in the graph, while these triangles will naturally arise in many networks (e.g....
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| Veröffentlicht in: | Theoretical population biology 2007-03, Vol.71 (2), p.160-173 |
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| container_title | Theoretical population biology |
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| creator | Trapman, Pieter |
| description | One way to describe the spread of an infection on a network is by approximating the network by a random graph. However, the usual way of constructing a random graph does not give any control over the number of triangles in the graph, while these triangles will naturally arise in many networks (e.g. in social networks).
In this paper, random graphs with a given degree distribution and a given expected number of triangles are constructed.
By using these random graphs we analyze the spread of two types of infection on a network: infections with a fixed infectious period and infections for which an infective individual will infect all of its susceptible neighbors or none. These two types of infection can be used to give upper and lower bounds for
R
0
, the probability of extinction and other measures of dynamics of infections with more general infectious periods. |
| doi_str_mv | 10.1016/j.tpb.2006.11.002 |
| format | Article |
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In this paper, random graphs with a given degree distribution and a given expected number of triangles are constructed.
By using these random graphs we analyze the spread of two types of infection on a network: infections with a fixed infectious period and infections for which an infective individual will infect all of its susceptible neighbors or none. These two types of infection can be used to give upper and lower bounds for
R
0
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In this paper, random graphs with a given degree distribution and a given expected number of triangles are constructed.
By using these random graphs we analyze the spread of two types of infection on a network: infections with a fixed infectious period and infections for which an infective individual will infect all of its susceptible neighbors or none. These two types of infection can be used to give upper and lower bounds for
R
0
, the probability of extinction and other measures of dynamics of infections with more general infectious periods.</description><subject>Communicable Diseases - epidemiology</subject><subject>Communicable Diseases - transmission</subject><subject>Disease Outbreaks</subject><subject>Epidemics</subject><subject>Humans</subject><subject>Mathematics</subject><subject>Models, Statistical</subject><subject>Neural Networks (Computer)</subject><subject>Percolation</subject><subject>Probability</subject><subject>Random graphs</subject><subject>Social Support</subject><issn>0040-5809</issn><issn>1096-0325</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2007</creationdate><recordtype>article</recordtype><sourceid>EIF</sourceid><recordid>eNqFkMtOwzAQRS0EoqXwAWxQVuwSZpyHHbFCiJdUqRtYW449ES55Eaeg_j2uWokdbGY2594ZHcYuERIELG7WyTRUCQcoEsQEgB-xOUJZxJDy_JjNATKIcwnljJ15vwYAiWl6ymYoOOdSlHOGqy7SnW62kzO6ifQwjL027-SjqY9ocJZaZ3zUd1FH03c_fvhzdlLrxtPFYS_Y2-PD6_1zvFw9vdzfLWOTZXKKdQU1N6bgkFMtSksgrLBFKaoMwm0DWUla5ClhVVlbhyGt5BWHGnMsoEgX7HrfGz763JCfVOu8oabRHfUbrwpZSiHE_yCWuci5TAOIe9CMvfcj1WoYXavHrUJQO6FqrYJQtROqEFUQGjJXh_JN1ZL9TRwMBuB2D1Bw8eVoVN446gxZN5KZlO3dH_U_RbGFig</recordid><startdate>20070301</startdate><enddate>20070301</enddate><creator>Trapman, Pieter</creator><general>Elsevier Inc</general><scope>CGR</scope><scope>CUY</scope><scope>CVF</scope><scope>ECM</scope><scope>EIF</scope><scope>NPM</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SN</scope><scope>C1K</scope><scope>7X8</scope></search><sort><creationdate>20070301</creationdate><title>On analytical approaches to epidemics on networks</title><author>Trapman, Pieter</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c448t-ab0f2cc6205ef79de07d7d697b40228c049ea753e1bbddfbbd8d82b20f1516063</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2007</creationdate><topic>Communicable Diseases - epidemiology</topic><topic>Communicable Diseases - transmission</topic><topic>Disease Outbreaks</topic><topic>Epidemics</topic><topic>Humans</topic><topic>Mathematics</topic><topic>Models, Statistical</topic><topic>Neural Networks (Computer)</topic><topic>Percolation</topic><topic>Probability</topic><topic>Random graphs</topic><topic>Social Support</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Trapman, Pieter</creatorcontrib><collection>Medline</collection><collection>MEDLINE</collection><collection>MEDLINE (Ovid)</collection><collection>MEDLINE</collection><collection>MEDLINE</collection><collection>PubMed</collection><collection>CrossRef</collection><collection>Ecology Abstracts</collection><collection>Environmental Sciences and Pollution Management</collection><collection>MEDLINE - Academic</collection><jtitle>Theoretical population biology</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Trapman, Pieter</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On analytical approaches to epidemics on networks</atitle><jtitle>Theoretical population biology</jtitle><addtitle>Theor Popul Biol</addtitle><date>2007-03-01</date><risdate>2007</risdate><volume>71</volume><issue>2</issue><spage>160</spage><epage>173</epage><pages>160-173</pages><issn>0040-5809</issn><eissn>1096-0325</eissn><abstract>One way to describe the spread of an infection on a network is by approximating the network by a random graph. However, the usual way of constructing a random graph does not give any control over the number of triangles in the graph, while these triangles will naturally arise in many networks (e.g. in social networks).
In this paper, random graphs with a given degree distribution and a given expected number of triangles are constructed.
By using these random graphs we analyze the spread of two types of infection on a network: infections with a fixed infectious period and infections for which an infective individual will infect all of its susceptible neighbors or none. These two types of infection can be used to give upper and lower bounds for
R
0
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| ispartof | Theoretical population biology, 2007-03, Vol.71 (2), p.160-173 |
| issn | 0040-5809 1096-0325 |
| language | eng |
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| source | MEDLINE; Elsevier ScienceDirect Journals |
| subjects | Communicable Diseases - epidemiology Communicable Diseases - transmission Disease Outbreaks Epidemics Humans Mathematics Models, Statistical Neural Networks (Computer) Percolation Probability Random graphs Social Support |
| title | On analytical approaches to epidemics on networks |
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