How to distribute antidote to control epidemics
Identifieur interne : 001B76 ( Istex/Corpus ); précédent : 001B75; suivant : 001B77How to distribute antidote to control epidemics
Auteurs : Christian Borgs ; Jennifer Chayes ; Ayalvadi Ganesh ; Amin SaberiSource :
- Random Structures & Algorithms [ 1042-9832 ] ; 2010-09.
English descriptors
- Teeft :
- Algorithm, Amin saberi, Antidote, Average degree, Borgs, Constant factor, Constant infection rate, Contact process, Control epidemics, Cure rate, Cure rates, Current state, Discrete time chain, Epidemic, Epidemic threshold, Epidemic thresholds, Epidemiological networks, General graph, Healthy center, High probability, Infection, Initial condition, Inoculation scheme, Last step, Lemma, Long list, Long time, Microsoft research, Mutating viruses, Next lemma, Next theorem, Nite, Nite graph, Node, Normalization condition, Original chain, Other hand, Other words, Poisson clocks, Positive probability, Quadratic equation, Random structures, Random variables, Right hand side, Rigorous analysis, Single phase, Social networks, Standard contact process, Star graph, State transitions, Stochastic processes, Survival time, Technological networks, Total amount, Wiley periodicals, Worm.
Abstract
We give a rigorous analysis of variations of the contact process on a finite graph in which the cure rate is allowed to vary from one vertex to the next, and even to depend on the current state of the system. In particular, we study the epidemic threshold in the models where the cure rate is proportional to the degree of the node or when it is proportional to the number of its infected neighbors. © 2010 Wiley Periodicals, Inc. Random Struct. Alg., 2010
Url:
DOI: 10.1002/rsa.20315
Links to Exploration step
ISTEX:2714DD900098A8045CC2CFB68B2E485FBCF82750Le document en format XML
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Alg.</title></titleGroup></publicationMeta><publicationMeta level="part" position="20"><doi origin="wiley" registered="yes">10.1002/rsa.v37:2</doi><numberingGroup><numbering type="journalVolume" number="37">37</numbering><numbering type="journalIssue">2</numbering></numberingGroup><coverDate startDate="2010-09">September 2010</coverDate></publicationMeta><publicationMeta level="unit" type="article" position="30" status="forIssue"><doi origin="wiley" registered="yes">10.1002/rsa.20315</doi><idGroup><id type="unit" value="RSA20315"></id></idGroup><countGroup><count type="pageTotal" number="19"></count></countGroup><copyright ownership="publisher">Copyright © 2010 Wiley Periodicals, Inc.</copyright><eventGroup><event type="manuscriptReceived" date="2008-09-13"></event><event type="manuscriptAccepted" date="2009-03-03"></event><event type="firstOnline" date="2010-02-18"></event><event type="publishedOnlineFinalForm" date="2010-07-13"></event><event type="publishedOnlineAcceptedOrEarlyUnpaginated" date="2010-02-18"></event><event type="xmlConverted" agent="Converter:JWSART34_TO_WML3G version:2.3.27 mode:FullText source:HeaderRef result:HeaderRef" date="2010-11-22"></event><event type="xmlConverted" agent="Converter:WILEY_ML3G_TO_WILEY_ML3GV2 version:3.8.8" date="2014-02-08"></event><event type="xmlConverted" agent="Converter:WML3G_To_WML3G version:4.1.7 mode:FullText,remove_FC" date="2014-11-03"></event></eventGroup><numberingGroup><numbering type="pageFirst">204</numbering><numbering type="pageLast">222</numbering></numberingGroup><correspondenceTo>Department of Management Science and Engineering, Institute for Computational and Mathematical Engineering, Stanford University, Stanford, California 94305</correspondenceTo><linkGroup><link type="toTypesetVersion" href="file:RSA.RSA20315.pdf"></link></linkGroup></publicationMeta><contentMeta><countGroup><count type="figureTotal" number="0"></count><count type="tableTotal" number="0"></count><count type="referenceTotal" number="26"></count><count type="wordTotal" number="769"></count></countGroup><titleGroup><title type="main" xml:lang="en">How to distribute antidote to control epidemics</title><title type="short" xml:lang="en">How to Distribute Antidote to Control Epidemics</title></titleGroup><creators><creator xml:id="au1" creatorRole="author" affiliationRef="#af1"><personName><givenNames>Christian</givenNames><familyName>Borgs</familyName></personName></creator><creator xml:id="au2" creatorRole="author" affiliationRef="#af1"><personName><givenNames>Jennifer</givenNames><familyName>Chayes</familyName></personName></creator><creator xml:id="au3" creatorRole="author" affiliationRef="#af2"><personName><givenNames>Ayalvadi</givenNames><familyName>Ganesh</familyName></personName></creator><creator xml:id="au4" creatorRole="author" affiliationRef="#af3" corresponding="yes"><personName><givenNames>Amin</givenNames><familyName>Saberi</familyName></personName><contactDetails><email>saberi@stanford.edu</email></contactDetails></creator></creators><affiliationGroup><affiliation xml:id="af1" countryCode="US" type="organization"><unparsedAffiliation>Microsoft Research, One Memorial Drive, Cambridge, Massachusetts 02142</unparsedAffiliation></affiliation><affiliation xml:id="af2" countryCode="GB" type="organization"><unparsedAffiliation>Department of Mathematics, University of Bristol, Bristol BS8 1TW, UK</unparsedAffiliation></affiliation><affiliation xml:id="af3" countryCode="US" type="organization"><unparsedAffiliation>Department of Management Science and Engineering, Institute for Computational and Mathematical Engineering, Stanford University, Stanford, California 94305</unparsedAffiliation></affiliation></affiliationGroup><keywordGroup xml:lang="en" type="author"><keyword xml:id="kwd1">contact process</keyword><keyword xml:id="kwd2">networks</keyword><keyword xml:id="kwd3">controlling epidemics</keyword></keywordGroup><fundingInfo><fundingAgency>National Science Foundation</fundingAgency></fundingInfo><abstractGroup><abstract type="main" xml:lang="en"><title type="main">Abstract</title><p>We give a rigorous analysis of variations of the contact process on a finite graph in which the cure rate is allowed to vary from one vertex to the next, and even to depend on the current state of the system. In particular, we study the epidemic threshold in the models where the cure rate is proportional to the degree of the node or when it is proportional to the number of its infected neighbors. © 2010 Wiley Periodicals, Inc. Random Struct. Alg., 2010</p></abstract></abstractGroup></contentMeta></header></component></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>How to distribute antidote to control epidemics</title></titleInfo><titleInfo type="abbreviated" lang="en"><title>How to Distribute Antidote to Control Epidemics</title></titleInfo><titleInfo type="alternative" contentType="CDATA" lang="en"><title>How to distribute antidote to control epidemics</title></titleInfo><name type="personal"><namePart type="given">Christian</namePart><namePart type="family">Borgs</namePart><affiliation>Microsoft Research, One Memorial Drive, Cambridge, Massachusetts 02142</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Jennifer</namePart><namePart type="family">Chayes</namePart><affiliation>Microsoft Research, One Memorial Drive, Cambridge, Massachusetts 02142</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Ayalvadi</namePart><namePart type="family">Ganesh</namePart><affiliation>Department of Mathematics, University of Bristol, Bristol BS8 1TW, UK</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Amin</namePart><namePart type="family">Saberi</namePart><affiliation>Department of Management Science and Engineering, Institute for Computational and Mathematical Engineering, Stanford University, Stanford, California 94305</affiliation><affiliation>E-mail: saberi@stanford.edu</affiliation><affiliation>Correspondence address: Department of Management Science and Engineering, Institute for Computational and Mathematical Engineering, Stanford University, Stanford, California 94305</affiliation><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre type="article" displayLabel="article" authority="ISTEX" authorityURI="https://content-type.data.istex.fr" valueURI="https://content-type.data.istex.fr/ark:/67375/XTP-6N5SZHKN-D">article</genre><originInfo><publisher>Wiley Subscription Services, Inc., A Wiley Company</publisher><place><placeTerm type="text">Hoboken</placeTerm></place><dateIssued encoding="w3cdtf">2010-09</dateIssued><dateCaptured encoding="w3cdtf">2008-09-13</dateCaptured><dateValid encoding="w3cdtf">2009-03-03</dateValid><copyrightDate encoding="w3cdtf">2010</copyrightDate></originInfo><language><languageTerm type="code" authority="rfc3066">en</languageTerm><languageTerm type="code" authority="iso639-2b">eng</languageTerm></language><physicalDescription><extent unit="figures">0</extent><extent unit="tables">0</extent><extent unit="references">26</extent><extent unit="words">769</extent></physicalDescription><abstract lang="en">We give a rigorous analysis of variations of the contact process on a finite graph in which the cure rate is allowed to vary from one vertex to the next, and even to depend on the current state of the system. In particular, we study the epidemic threshold in the models where the cure rate is proportional to the degree of the node or when it is proportional to the number of its infected neighbors. © 2010 Wiley Periodicals, Inc. Random Struct. Alg., 2010</abstract><note type="funding">National Science Foundation</note><subject lang="en"><genre>keywords</genre><topic>contact process</topic><topic>networks</topic><topic>controlling epidemics</topic></subject><relatedItem type="host"><titleInfo><title>Random Structures & Algorithms</title></titleInfo><titleInfo type="abbreviated"><title>Random Struct. Alg.</title></titleInfo><genre type="journal" authority="ISTEX" authorityURI="https://publication-type.data.istex.fr" valueURI="https://publication-type.data.istex.fr/ark:/67375/JMC-0GLKJH51-B">journal</genre><identifier type="ISSN">1042-9832</identifier><identifier type="eISSN">1098-2418</identifier><identifier type="DOI">10.1002/(ISSN)1098-2418</identifier><identifier type="PublisherID">RSA</identifier><part><date>2010</date><detail type="volume"><caption>vol.</caption><number>37</number></detail><detail type="issue"><caption>no.</caption><number>2</number></detail><extent unit="pages"><start>204</start><end>222</end><total>19</total></extent></part></relatedItem><relatedItem type="references" displayLabel="cit1"><titleInfo><title>A random graph model for power law graphs</title></titleInfo><name type="personal"><namePart type="given">W.</namePart><namePart type="family">Aiello</namePart><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">F.</namePart><namePart type="family">Chung</namePart><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">L.</namePart><namePart type="family">Lu</namePart><role><roleTerm type="text">author</roleTerm></role></name><genre>journal-article</genre><note type="citation/reference">W.Aiello,F.Chung, and L.Lu, A random graph model for power law graphs, Exp Math 10 ( 2001), 53–66.</note><part><date>2001</date><detail type="volume"><caption>vol.</caption><number>10</number></detail><extent unit="pages"><start>53</start><end>66</end></extent></part><relatedItem type="host"><titleInfo><title>Exp Math</title></titleInfo><part><date>2001</date><detail type="volume"><caption>vol.</caption><number>10</number></detail><extent unit="pages"><start>53</start><end>66</end></extent></part></relatedItem></relatedItem><relatedItem type="references" displayLabel="cit2"><titleInfo><title>Emergence of scaling in random networks</title></titleInfo><name type="personal"><namePart type="given">A.‐L.</namePart><namePart type="family">Barabási</namePart><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">R.</namePart><namePart type="family">Albert</namePart><role><roleTerm type="text">author</roleTerm></role></name><genre>journal-article</genre><note type="citation/reference">A.‐L.Barabási and R.Albert, Emergence of scaling in random networks, Science 286 ( 1999), 509–512.</note><part><date>1999</date><detail type="volume"><caption>vol.</caption><number>286</number></detail><extent unit="pages"><start>509</start><end>512</end></extent></part><relatedItem type="host"><titleInfo><title>Science</title></titleInfo><part><date>1999</date><detail type="volume"><caption>vol.</caption><number>286</number></detail><extent unit="pages"><start>509</start><end>512</end></extent></part></relatedItem></relatedItem><relatedItem type="references" displayLabel="cit3"><titleInfo><title>On the spread of viruses on the internet, Soda '05: Proceedings of the sixteenth annual acm‐siam symposium on discrete algorithms</title></titleInfo><name type="personal"><namePart type="given">N.</namePart><namePart type="family">Berger</namePart><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">C.</namePart><namePart type="family">Borgs</namePart><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">J.</namePart><namePart type="family">Chayes</namePart><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">A.</namePart><namePart type="family">Saberi</namePart><role><roleTerm type="text">author</roleTerm></role></name><genre>other</genre><part><date>2005</date></part></relatedItem><relatedItem type="references" displayLabel="cit4"><titleInfo><title>The degree sequence of a scale‐free random graph process</title></titleInfo><name type="personal"><namePart type="given">B.</namePart><namePart type="family">Bollobás</namePart><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">O.</namePart><namePart type="family">Riordan</namePart><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">J.</namePart><namePart type="family">Spencer</namePart><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">G.</namePart><namePart type="family">Tusnady</namePart><role><roleTerm type="text">author</roleTerm></role></name><genre>journal-article</genre><note type="citation/reference">B.Bollobás,O.Riordan,J.Spencer, and G.Tusnady, The degree sequence of a scale‐free random graph process, Random Struct Algorithms 18 ( 2001), 279–290.</note><part><date>2001</date><detail type="volume"><caption>vol.</caption><number>18</number></detail><extent unit="pages"><start>279</start><end>290</end></extent></part><relatedItem type="host"><titleInfo><title>Random Struct Algorithms</title></titleInfo><part><date>2001</date><detail type="volume"><caption>vol.</caption><number>18</number></detail><extent unit="pages"><start>279</start><end>290</end></extent></part></relatedItem></relatedItem><relatedItem type="references" displayLabel="cit5"><titleInfo><title>Network analysis of cattle movement in Great Britain</title></titleInfo><name type="personal"><namePart type="given">R.</namePart><namePart type="family">Christley</namePart><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">S.</namePart><namePart type="family">Robinson</namePart><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">R.</namePart><namePart type="family">Lysons</namePart><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">N.</namePart><namePart type="family">French</namePart><role><roleTerm type="text">author</roleTerm></role></name><genre>journal-article</genre><note type="citation/reference">R.Christley,S.Robinson,R.Lysons, and N.French, Network analysis of cattle movement in Great Britain, Proc Soc Vet Epidemiol Prev Med 81 ( 2005), 21–37.</note><part><date>2005</date><detail type="volume"><caption>vol.</caption><number>81</number></detail><extent unit="pages"><start>21</start><end>37</end></extent></part><relatedItem type="host"><titleInfo><title>Proc Soc Vet Epidemiol Prev Med</title></titleInfo><part><date>2005</date><detail type="volume"><caption>vol.</caption><number>81</number></detail><extent unit="pages"><start>21</start><end>37</end></extent></part></relatedItem></relatedItem><relatedItem type="references" displayLabel="cit6"><titleInfo><title>R.Durrett,Essentials of Stochastic Processes,Springer,New York,1999.</title></titleInfo><note type="citation/reference">R.Durrett, Essentials of Stochastic Processes, Springer, New York, 1999.</note><name type="personal"><namePart type="given">R.</namePart><namePart type="family">Durrett</namePart><role><roleTerm type="text">author</roleTerm></role></name><genre>book</genre><originInfo><publisher>Springer</publisher><place><placeTerm type="text">New York</placeTerm></place></originInfo><part><date>1999</date></part></relatedItem><relatedItem type="references" displayLabel="cit7"><titleInfo><title>Optimizing the control of disease infestations at the landscape scale</title></titleInfo><name type="personal"><namePart type="given">G.</namePart><namePart type="family">Forster</namePart><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">C. A.</namePart><namePart type="family">Gilligan</namePart><role><roleTerm type="text">author</roleTerm></role></name><genre>journal-article</genre><note type="citation/reference">G.Forster, and C. A.Gilligan, Optimizing the control of disease infestations at the landscape scale, Proc Natl Acad Sci USA 104 ( 2007), 4984–4989.</note><part><date>2007</date><detail type="volume"><caption>vol.</caption><number>104</number></detail><extent unit="pages"><start>4984</start><end>4989</end></extent></part><relatedItem type="host"><titleInfo><title>Proc Natl Acad Sci USA</title></titleInfo><part><date>2007</date><detail type="volume"><caption>vol.</caption><number>104</number></detail><extent unit="pages"><start>4984</start><end>4989</end></extent></part></relatedItem></relatedItem><relatedItem type="references" displayLabel="cit8"><titleInfo><title>The effect of network topology on the spread of epidemics, In Proceedings of 24th IEEE Conference on Computer Communications (INFOCOM)</title></titleInfo><name type="personal"><namePart type="given">A.</namePart><namePart type="family">Ganesh</namePart><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">L.</namePart><namePart type="family">Massoulie</namePart><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">D.</namePart><namePart type="family">Towsley</namePart><role><roleTerm type="text">author</roleTerm></role></name><genre>other</genre><part><date>2005</date></part></relatedItem><relatedItem type="references" displayLabel="cit9"><titleInfo><title>Conductance and congestion in power law graphs</title></titleInfo><name type="personal"><namePart type="given">C.</namePart><namePart type="family">Gkantsidis</namePart><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">M.</namePart><namePart type="family">Mihail</namePart><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">A.</namePart><namePart type="family">Saberi</namePart><role><roleTerm type="text">author</roleTerm></role></name><genre>journal-article</genre><note type="citation/reference">C.Gkantsidis,M.Mihail, and A.Saberi, Conductance and congestion in power law graphs, SIGMETRICS Perform Eval Rev 31 ( 2003), 148–159.</note><part><date>2003</date><detail type="volume"><caption>vol.</caption><number>31</number></detail><extent unit="pages"><start>148</start><end>159</end></extent></part><relatedItem type="host"><titleInfo><title>SIGMETRICS Perform Eval Rev</title></titleInfo><part><date>2003</date><detail type="volume"><caption>vol.</caption><number>31</number></detail><extent unit="pages"><start>148</start><end>159</end></extent></part></relatedItem></relatedItem><relatedItem type="references" displayLabel="cit10"><titleInfo><title>Networks and epidemic models</title></titleInfo><name type="personal"><namePart type="given">M. J.</namePart><namePart type="family">Keeling</namePart><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">K. T. D.</namePart><namePart type="family">Eames</namePart><role><roleTerm type="text">author</roleTerm></role></name><genre>journal-article</genre><note type="citation/reference">M. J.Keeling and K. T. D.Eames, Networks and epidemic models, J Royal Soc Interface 2 ( 2005), 295–307.</note><part><date>2005</date><detail type="volume"><caption>vol.</caption><number>2</number></detail><extent unit="pages"><start>295</start><end>307</end></extent></part><relatedItem type="host"><titleInfo><title>J Royal Soc Interface</title></titleInfo><part><date>2005</date><detail type="volume"><caption>vol.</caption><number>2</number></detail><extent unit="pages"><start>295</start><end>307</end></extent></part></relatedItem></relatedItem><relatedItem type="references" displayLabel="cit11"><titleInfo><title>Recent worms: A survey and trends</title></titleInfo><name type="personal"><namePart type="given">D. M.</namePart><namePart type="family">Kienzle</namePart><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">M. C.</namePart><namePart type="family">Elder</namePart><role><roleTerm type="text">author</roleTerm></role></name><genre>other</genre><part><date>2003</date></part></relatedItem><relatedItem type="references" displayLabel="cit12"><titleInfo><title>Infectious disease control using contact tracing in random and scale‐free networks</title></titleInfo><name type="personal"><namePart type="given">I. Z.</namePart><namePart type="family">Kiss</namePart><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">D. M.</namePart><namePart type="family">Green</namePart><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">R. R.</namePart><namePart type="family">Kao</namePart><role><roleTerm type="text">author</roleTerm></role></name><genre>journal-article</genre><note type="citation/reference">I. Z.Kiss,D. M.Green, and R. R.Kao, Infectious disease control using contact tracing in random and scale‐free networks, J Royal Soc Interface ( 2006), 55–62.</note><part><date>2006</date><extent unit="pages"><start>55</start><end>62</end></extent></part><relatedItem type="host"><titleInfo><title>J Royal Soc Interface</title></titleInfo><part><date>2006</date><extent unit="pages"><start>55</start><end>62</end></extent></part></relatedItem></relatedItem><relatedItem type="references" displayLabel="cit13"><titleInfo><title>G. F.Lawler,Introduction to Stochastic Processes,CRC Press,New York,1995.</title></titleInfo><note type="citation/reference">G. F.Lawler, Introduction to Stochastic Processes, CRC Press, New York, 1995.</note><name type="personal"><namePart type="given">G. F.</namePart><namePart type="family">Lawler</namePart><role><roleTerm type="text">author</roleTerm></role></name><genre>book</genre><originInfo><publisher>CRC Press</publisher><place><placeTerm type="text">New York</placeTerm></place></originInfo><part><date>1995</date></part></relatedItem><relatedItem type="references" displayLabel="cit14"><titleInfo><title>T. M.Liggett,Stochastic interacting systems: Contact, voter and exclusion processes, Grundlehren der Mathematischen Wissenschaften (Fundamental Principles of Mathematical Sciences), Vol.324,Springer‐Verlag,Berlin,1999.</title></titleInfo><genre>book</genre><originInfo><publisher>Springer‐Verlag</publisher></originInfo><part><date>1999</date></part></relatedItem><relatedItem type="references" displayLabel="cit15"><titleInfo><title>The web of human sexual contacts</title></titleInfo><name type="personal"><namePart type="given">F.</namePart><namePart type="family">Liljeros</namePart><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">C. R.</namePart><namePart type="family">Edling</namePart><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">L. A. N.</namePart><namePart type="family">Amaral</namePart><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">H. E.</namePart><namePart type="family">Stanley</namePart><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Y.</namePart><namePart type="family">Aberg</namePart><role><roleTerm type="text">author</roleTerm></role></name><genre>journal-article</genre><note type="citation/reference">F.Liljeros,C. R.Edling,L. A. N.Amaral,H. E.Stanley, and Y.Aberg, The web of human sexual contacts, Nature 411 ( 2001), 907.</note><part><date>2001</date><detail type="volume"><caption>vol.</caption><number>411</number></detail><extent unit="pages"><start>907</start></extent></part><relatedItem type="host"><titleInfo><title>Nature</title></titleInfo><part><date>2001</date><detail type="volume"><caption>vol.</caption><number>411</number></detail><extent unit="pages"><start>907</start></extent></part></relatedItem></relatedItem><relatedItem type="references" displayLabel="cit16"><titleInfo><title>Network theory and sars: Predicting outbreak diversity</title></titleInfo><name type="personal"><namePart type="given">L. A.</namePart><namePart type="family">Meyers</namePart><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">B.</namePart><namePart type="family">Pourbohloul</namePart><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">M. E. J.</namePart><namePart type="family">Newman</namePart><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">D. M.</namePart><namePart type="family">Skowronski</namePart><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">R. C.</namePart><namePart type="family">Brunham</namePart><role><roleTerm type="text">author</roleTerm></role></name><genre>journal-article</genre><note type="citation/reference">L. A.Meyers,B.Pourbohloul,M. E. J.Newman,D. M.Skowronski, and R. C.Brunham, Network theory and sars: Predicting outbreak diversity, J Theor Biol ( 2005), 71–81.</note><part><date>2005</date><extent unit="pages"><start>71</start><end>81</end></extent></part><relatedItem type="host"><titleInfo><title>J Theor Biol</title></titleInfo><part><date>2005</date><extent unit="pages"><start>71</start><end>81</end></extent></part></relatedItem></relatedItem><relatedItem type="references" displayLabel="cit17"><titleInfo><title>On certain connectivity properties of the Internet topology</title></titleInfo><name type="personal"><namePart type="given">M.</namePart><namePart type="family">Mihail</namePart><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">C.</namePart><namePart type="family">Papadimitriou</namePart><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">A.</namePart><namePart type="family">Saberi</namePart><role><roleTerm type="text">author</roleTerm></role></name><genre>journal-article</genre><note type="citation/reference">M.Mihail,C.Papadimitriou, and A.Saberi, On certain connectivity properties of the Internet topology, J Comput Syst Sci ( 2003), 28–35.</note><part><date>2003</date><extent unit="pages"><start>28</start><end>35</end></extent></part><relatedItem type="host"><titleInfo><title>J Comput Syst Sci</title></titleInfo><part><date>2003</date><extent unit="pages"><start>28</start><end>35</end></extent></part></relatedItem></relatedItem><relatedItem type="references" displayLabel="cit18"><titleInfo><title>Code‐Red: a case study on the spread and victims of an internet worm</title></titleInfo><name type="personal"><namePart type="given">D.</namePart><namePart type="family">Moore</namePart><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">C.</namePart><namePart type="family">Shannon</namePart><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">K.</namePart><namePart type="family">Claffy</namePart><role><roleTerm type="text">author</roleTerm></role></name><genre>other</genre><part><date>2002</date></part></relatedItem><relatedItem type="references" displayLabel="cit19"><titleInfo><title>Epidemic spreading in scale‐free networks</title></titleInfo><name type="personal"><namePart type="given">R.</namePart><namePart type="family">Pastor‐Satorras</namePart><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">A.</namePart><namePart type="family">Vespignani</namePart><role><roleTerm type="text">author</roleTerm></role></name><genre>journal-article</genre><note type="citation/reference">R.Pastor‐Satorras and A.Vespignani, Epidemic spreading in scale‐free networks, Phys Rev Lett 86 ( 2001), 3200–3203.</note><part><date>2001</date><detail type="volume"><caption>vol.</caption><number>86</number></detail><extent unit="pages"><start>3200</start><end>3203</end></extent></part><relatedItem type="host"><titleInfo><title>Phys Rev Lett</title></titleInfo><part><date>2001</date><detail type="volume"><caption>vol.</caption><number>86</number></detail><extent unit="pages"><start>3200</start><end>3203</end></extent></part></relatedItem></relatedItem><relatedItem type="references" displayLabel="cit20"><titleInfo><title>Epidemic dynamics in finite scale‐free networks</title></titleInfo><name type="personal"><namePart type="given">R.</namePart><namePart type="family">Pastor‐Satorras</namePart><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">A.</namePart><namePart type="family">Vespignani</namePart><role><roleTerm type="text">author</roleTerm></role></name><genre>journal-article</genre><note type="citation/reference">R.Pastor‐Satorras and A.Vespignani, Epidemic dynamics in finite scale‐free networks, Phys Rev E 65 ( 2002), 035108–035112.</note><part><date>2002</date><detail type="volume"><caption>vol.</caption><number>65</number></detail><extent unit="pages"><start>035108</start><end>035112</end></extent></part><relatedItem type="host"><titleInfo><title>Phys Rev E</title></titleInfo><part><date>2002</date><detail type="volume"><caption>vol.</caption><number>65</number></detail><extent unit="pages"><start>035108</start><end>035112</end></extent></part></relatedItem></relatedItem><relatedItem type="references" displayLabel="cit21"><titleInfo><title>A general theory of bibliometric and other cumulative advantage processes</title></titleInfo><name type="personal"><namePart type="given">D. J.</namePart><namePart type="family">Price</namePart><role><roleTerm type="text">author</roleTerm></role></name><genre>journal-article</genre><note type="citation/reference">D. J.Price, A general theory of bibliometric and other cumulative advantage processes, J Am Soc Inform Sci 27 ( 1976), 292–306.</note><part><date>1976</date><detail type="volume"><caption>vol.</caption><number>27</number></detail><extent unit="pages"><start>292</start><end>306</end></extent></part><relatedItem type="host"><titleInfo><title>J Am Soc Inform Sci</title></titleInfo><part><date>1976</date><detail type="volume"><caption>vol.</caption><number>27</number></detail><extent unit="pages"><start>292</start><end>306</end></extent></part></relatedItem></relatedItem><relatedItem type="references" displayLabel="cit22"><titleInfo><title>The contact process on finite homogeneous trees</title></titleInfo><name type="personal"><namePart type="given">A.</namePart><namePart type="family">Stacey</namePart><role><roleTerm type="text">author</roleTerm></role></name><genre>journal-article</genre><note type="citation/reference">A.Stacey, The contact process on finite homogeneous trees, Probab Theory Relat Fields 121 ( 2001), 551–576.</note><part><date>2001</date><detail type="volume"><caption>vol.</caption><number>121</number></detail><extent unit="pages"><start>551</start><end>576</end></extent></part><relatedItem type="host"><titleInfo><title>Probab Theory Relat Fields</title></titleInfo><part><date>2001</date><detail type="volume"><caption>vol.</caption><number>121</number></detail><extent unit="pages"><start>551</start><end>576</end></extent></part></relatedItem></relatedItem><relatedItem type="references" displayLabel="cit23"><titleInfo><title>The existence of an intermediate phase for the contact process on trees</title></titleInfo><name type="personal"><namePart type="given">A. M.</namePart><namePart type="family">Stacey</namePart><role><roleTerm type="text">author</roleTerm></role></name><genre>journal-article</genre><note type="citation/reference">A. M.Stacey, The existence of an intermediate phase for the contact process on trees, Ann Probab 24 ( 1996), 1711–1726.</note><part><date>1996</date><detail type="volume"><caption>vol.</caption><number>24</number></detail><extent unit="pages"><start>1711</start><end>1726</end></extent></part><relatedItem type="host"><titleInfo><title>Ann Probab</title></titleInfo><part><date>1996</date><detail type="volume"><caption>vol.</caption><number>24</number></detail><extent unit="pages"><start>1711</start><end>1726</end></extent></part></relatedItem></relatedItem><relatedItem type="references" displayLabel="cit24"><titleInfo><title>How to own the internet in your spare time</title></titleInfo><name type="personal"><namePart type="given">S.</namePart><namePart type="family">Staniford</namePart><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">V.</namePart><namePart type="family">Paxson</namePart><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">N.</namePart><namePart type="family">Weaver</namePart><role><roleTerm type="text">author</roleTerm></role></name><genre>other</genre><part><date>2002</date></part></relatedItem><relatedItem type="references" displayLabel="cit25"><titleInfo><title>Modeling of contact tracing in social networks</title></titleInfo><name type="personal"><namePart type="given">L. S.</namePart><namePart type="family">Tsimring</namePart><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">R.</namePart><namePart type="family">Huerta</namePart><role><roleTerm type="text">author</roleTerm></role></name><genre>journal-article</genre><note type="citation/reference">L. S.Tsimring and R.Huerta, Modeling of contact tracing in social networks, Phys A: Stat Mech Appl 325 ( 2003), 33–39.</note><part><date>2003</date><detail type="volume"><caption>vol.</caption><number>325</number></detail><extent unit="pages"><start>33</start><end>39</end></extent></part><relatedItem type="host"><titleInfo><title>Phys A: Stat Mech Appl</title></titleInfo><part><date>2003</date><detail type="volume"><caption>vol.</caption><number>325</number></detail><extent unit="pages"><start>33</start><end>39</end></extent></part></relatedItem></relatedItem><relatedItem type="references" displayLabel="cit26"><titleInfo><title>Designing a contact process: The piecewise‐homogeneous process on a finite set with applications</title></titleInfo><name type="personal"><namePart type="given">A.</namePart><namePart type="family">Wagner</namePart><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">V.</namePart><namePart type="family">Anantharam</namePart><role><roleTerm type="text">author</roleTerm></role></name><genre>journal-article</genre><note type="citation/reference">A.Wagner and V.Anantharam, Designing a contact process: The piecewise‐homogeneous process on a finite set with applications, Stoch Proc Appl 115 ( 2005), 117–153.</note><part><date>2005</date><detail type="volume"><caption>vol.</caption><number>115</number></detail><extent unit="pages"><start>117</start><end>153</end></extent></part><relatedItem type="host"><titleInfo><title>Stoch Proc Appl</title></titleInfo><part><date>2005</date><detail type="volume"><caption>vol.</caption><number>115</number></detail><extent unit="pages"><start>117</start><end>153</end></extent></part></relatedItem></relatedItem><identifier type="istex">2714DD900098A8045CC2CFB68B2E485FBCF82750</identifier><identifier type="ark">ark:/67375/WNG-52B6ZPKP-T</identifier><identifier type="DOI">10.1002/rsa.20315</identifier><identifier type="ArticleID">RSA20315</identifier><accessCondition type="use and reproduction" contentType="copyright">Copyright © 2010 Wiley Periodicals, Inc.</accessCondition><recordInfo><recordContentSource authority="ISTEX" authorityURI="https://loaded-corpus.data.istex.fr" valueURI="https://loaded-corpus.data.istex.fr/ark:/67375/XBH-L0C46X92-X">wiley</recordContentSource><recordOrigin>Converted from (version ) to MODS version 3.6.</recordOrigin><recordCreationDate encoding="w3cdtf">2019-11-16</recordCreationDate></recordInfo></mods><json:item><extension>json</extension><original>false</original><mimetype>application/json</mimetype><uri>https://api.istex.fr/ark:/67375/WNG-52B6ZPKP-T/record.json</uri></json:item></metadata><serie></serie></istex></record>Pour manipuler ce document sous Unix (Dilib)
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