Document Zbl 1246.62207

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J. Stat.</a> <a href="/?q=in%3A304460" title="Articles in this Issue">38, No. 3, 600-616 (2011)</a>. </div> <div class="abstract">Summary: We estimate the parameters of a simple random network and a stochastic epidemic on that network using data consisting of recovery times of infected hosts. The SEIR epidemic model we fit has exponentially distributed transmission times with gamma distributed exposed and infectious periods on a network where every edge exists with the same probability, independent of other edges. We employ a Bayesian framework and Markov chain Monte Carlo (MCMC) integration to make estimates of the joint posterior distribution of the model parameters. We discuss the accuracy of the parameter estimates under various prior assumptions and show that it is possible in many scientifically interesting cases to accurately recover the parameters. We demonstrate our approach by studying a measles outbreak in Hagelloch, Germany, in 1861 consisting of 188 affected individuals. We provide an R package to carry out these analyses, which is available publicly on the Comprehensive R Archive Network.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A6075239">Cited in <strong>18</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A62P10" title="MSC2020">62P10</a> </td> <td class="space"> Applications of statistics to biology and medical sciences; meta analysis </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A92D30" title="MSC2020">92D30</a> </td> <td class="space"> Epidemiology </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A62F15" title="MSC2020">62F15</a> </td> <td class="space"> Bayesian inference </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A05C80" title="MSC2020">05C80</a> </td> <td class="space"> Random graphs (graph-theoretic aspects) </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A65C40" title="MSC2020">65C40</a> </td> <td class="space"> Numerical analysis or methods applied to Markov chains </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A05C82" title="MSC2020">05C82</a> </td> <td class="space"> Small world graphs, complex networks (graph-theoretic aspects) </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A05C90" title="MSC2020">05C90</a> </td> <td class="space"> Applications of graph theory </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A62-04" title="MSC2020">62-04</a> </td> <td class="space"> Software, source code, etc. for problems pertaining to statistics </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3AErd%C5%91s-R%C3%A9nyi">Erdős-Rényi</a>; <a href="/?q=ut%3Aexponential+random+graph+model+%28ERGM%29">exponential random graph model (ERGM)</a>; <a href="/?q=ut%3AMCMC">MCMC</a>; <a href="/?q=ut%3Ameasles">measles</a>; <a href="/?q=ut%3Astochastic+SEIR+epidemic">stochastic SEIR epidemic</a>; <a href="/?q=ut%3A%5Ctexttt%7BR+package+epinet%7D"><span class="zbmathjax-texttt">R package epinet</span></a>; <a href="/?q=ut%3A%5Ctexttt%7BR+package+ergm%7D"><span class="zbmathjax-texttt">R package ergm</span></a></div> <div class="software"> <h3>Software:</h3><a href="/software/6777">ergm</a>; <a href="/software/771">R</a>; <a href="/software/24733">epinet</a>; <a href="/software/4351">CRAN</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1246.62207" data-ciurl="/ci/06075239" data-biburl="/bibtex/06075239.bib" data-amsurl="/amsrefs/06075239.bib" data-xmlurl="/xml/06075239.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/06075239.pdf" title="Zbl 1246.62207 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1111/j.1467-9469.2010.00721.x" aria-label="DOI for “Bayesian inference for contact networks given epidemic data”" title="10.1111/j.1467-9469.2010.00721.x">DOI</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Anderson, Directly transmitted infections diseases: control by vaccination, Science 215 pp 1053– (1982) · <a href="/1225.37099" class="nowrap">Zbl 1225.37099</a></td> </tr><tr> <td>[2]</td> <td class="space">Bailey, A simple stochastic epidemic, Biometrika 37 pp 193– (1950) · <a href="/0038.29104" class="nowrap">Zbl 0038.29104</a> · <a href="https://doi.org/10.1093/biomet/37.3-4.193" class="nowrap">doi:10.1093/biomet/37.3-4.193</a></td> </tr><tr> <td>[3]</td> <td class="space">Barthelemy, Dynamical patterns of epidemic outbreaks in complex heterogeneous networks, J. 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Assoc. 103 pp 248– (2008a) · <a href="/1471.62390" class="nowrap">Zbl 1471.62390</a></td> </tr><tr> <td>[12]</td> <td class="space">Hunter, ergm: a package to fit simulate and diagnose exponential-family models for networks, J. Stat. Softw. 24 pp 1– (2008b) · <a href="https://doi.org/10.18637/jss.v024.i03" class="nowrap">doi:10.18637/jss.v024.i03</a></td> </tr><tr> <td>[13]</td> <td class="space">Keeling, Networks and epidemic models, J. Roy. Soc. Interface 2 pp 295– (2005)</td> </tr><tr> <td>[14]</td> <td class="space">Keeling, Modeling infectious diseases in humans and animals, Clin. Infect. Dis. 47 pp 864– (2008) · <a href="/1279.92038" class="nowrap">Zbl 1279.92038</a></td> </tr><tr> <td>[15]</td> <td class="space">Kenah, Contact intervals, survival analysis of epidemic data, and estimation of R0, Arxiv preprint arXiv:0912.3330 (2009)</td> </tr><tr> <td>[16]</td> <td class="space">Kermack, A contribution to the mathematical theory of epidemics, Proc. R. Soc. Lond. Ser. A Math. 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Comput. 15 pp 315– (2005)</td> </tr><tr> <td>[20]</td> <td class="space">Oesterle , H. 1992 Statistiche Reanalyse einer Masernepidemiie 1861 in Hagelloch MD thesis Eberhard-Karls Universität</td> </tr><tr> <td>[21]</td> <td class="space">Pfeilsticker, Beiträge zur Pathologie der Masern mit besonderer Berücksichtigung der statistischen Verhältnisse (1863)</td> </tr><tr> <td>[22]</td> <td class="space">R Development Core Team, R: a language and environment for statistical computing (2010)</td> </tr><tr> <td>[23]</td> <td class="space">Rahmandad, Heterogeneity and network structure in the dynamics of diffusion: comparing agent-based and differential equation models, Manage. Sci. 54 pp 998– (2008)</td> </tr><tr> <td>[24]</td> <td class="space">Ray, Proceedings of the Joint Statistical Meetings: Conference Held in Denver, Colorado (2008)</td> </tr><tr> <td>[25]</td> <td class="space">Schenzle, An age-structured model of pre- and post-vaccination measles transmission, Math. Med. Biol. 1 pp 169– (1984) · <a href="/0611.92021" class="nowrap">Zbl 0611.92021</a></td> </tr><tr> <td>[26]</td> <td class="space">Snijders, Markov chain Monte Carlo estimation of exponential random graph models, J. Soc. Struct. 3 pp 1– (2002)</td> </tr><tr> <td>[27]</td> <td class="space">Volz, SIR dynamics in random networks with heterogeneous connectivity, J. Math. Biol. 56 pp 293– (2008) · <a href="/1143.92036" class="nowrap">Zbl 1143.92036</a></td> </tr></table> <div class="reference_disclaimer"> This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching. </div> </div></article> </div></div> </div> </div> <div class="clearfix"></div> </div> </div> <div id="foot"><div class="copyright"> © 2025 <a target="fiz" href="https://www.fiz-karlsruhe.de/en">FIZ Karlsruhe GmbH</a> <a href="/privacy-policy/">Privacy Policy</a> <a href="/legal-notices/">Legal Notices</a> <a href="/terms-conditions/">Terms & Conditions</a> <div class="info"> <ul class="nav"> <li class="mastodon"> <a href="https://mathstodon.xyz/@zbMATH" target="_blank" class="no-new-tab-icon"> <img src="/static/mastodon.png" title="zbMATH at Mathstodon (opens in new tab)" alt="Mastodon logo"> </a> </li> </ul> </div> </div> <div class="clearfix" style="height: 0px;"></div> </div> </div> <script src="https://static.zbmath.org/contrib/jquery/1.9.1/jquery.min.js"></script> <script src="https://static.zbmath.org/contrib/jquery-caret/1.5.2/jquery.caret.min.js"></script> <script src="/static/js/jquery-ui-1.10.1.custom.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap/v3.3.7zb1/js/bootstrap.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-lightbox/v0.7.0/bootstrap-lightbox.min.js"></script> <script src="https://static.zbmath.org/contrib/retina/unknown/retina.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-select/v1.13.14/js/bootstrap-select.min.js"></script> <script> var SCRIPT_ROOT = ""; </script> <script src="/static/scripts.js?v=20240926"> </script> <script src="https://static.zbmath.org/contrib/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script> <script type="text/x-mathjax-config"> MathJax.Hub.Config({ "HTML-CSS": { preferredFont: "TeX", availableFonts: [ "STIX", "TeX" ], linebreaks: { automatic: true }, EqnChunk: (MathJax.Hub.Browser.isMobile ? 10 : 50) }, tex2jax: { processEscapes: true, ignoreClass: "tex2jax_ignore|dno" }, TeX: { Macros: { Aut: "\\operatorname{Aut}", Hom: "\\operatorname{Hom}" }, noUndefined: { attributes: { mathcolor: "#039", //"red", mathbackground: "white", //"#FFEEEE", mathsize: "90%" } } }, messageStyle: "none" }); </script> <script type="text/javascript"> $(document).ready(function() { $("#MathInput").stop(true, true).keyup(function() { $.ajax({ url: "/mwsq/", type: "POST", data: { query : $("#MathInput").val() }, dataType: "text" }) .done(function(xml) { $("#MathPreview").html(xml); $(window).resize(); }); }); var press = jQuery.Event("keyup"); press.ctrlKey = false; press.which = 40; $("#MathInput").trigger(press); }); </script> <div id="new_tab_icon" style="display: none"> <span class="glyphicon glyphicon-new-window" aria-hidden="true"></span><span class="sr-only">(opens in new tab)</span></div> </body> </html>

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