Document Zbl 0823.92024

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A general model for an epidemic in a closed, homogeneously mixing population is presented. A construction of a sequence of such epidemics, indexed by the initial number of susceptibles $N$, from the limiting branching process is described. Strong convergence of the epidemic processes to the branching process is shown when the latter goes extinct. When the branching process does not go extinct, necessary and sufficient conditions on the sequence $(t_ N)$ for strong convergence over the time interval $[0, t_ N]$ are provided. <br class="zbmathjax-paragraph">Convergence of a wide variety of functionals of the epidemic process to corresponding functionals of the branching process is shown, and bounds are provided on the total variation distance for given $N$. The theory is illustrated by reference to the general stochastic epidemic. Generalisations to, for example, multipopulation epidemics are described briefly.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A735469">Cited in <strong>92</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><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%3A60J80" title="MSC2020">60J80</a> </td> <td class="space"> Branching processes (Galton-Watson, birth-and-death, etc.) </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A60F15" title="MSC2020">60F15</a> </td> <td class="space"> Strong limit theorems </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A60J85" title="MSC2020">60J85</a> </td> <td class="space"> Applications of branching processes </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A60K99" title="MSC2020">60K99</a> </td> <td class="space"> Special processes </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Acoupling">coupling</a>; <a href="/?q=ut%3Ageneral+branching+process">general branching process</a>; <a href="/?q=ut%3Aclosed+homogeneously+mixing+population">closed homogeneously mixing population</a>; <a href="/?q=ut%3Alimiting+branching+process">limiting branching process</a>; <a href="/?q=ut%3Atotal+variation+distance">total variation distance</a>; <a href="/?q=ut%3Ageneral+stochastic+epidemic">general stochastic epidemic</a>; <a href="/?q=ut%3Amultipopulation+epidemics">multipopulation epidemics</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 0823.92024" data-ciurl="/ci/00735469" data-biburl="/bibtex/00735469.bib" data-amsurl="/amsrefs/00735469.bib" data-xmlurl="/xml/00735469.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/00735469.pdf" title="Zbl 0823.92024 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/10.1016/0304-4149(94)00034-Q" aria-label="DOI for “Strong approximations for epidemic models”" title="10.1016/0304-4149(94)00034-Q">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">Aldous, D. 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