Document Zbl 0947.92017

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Biosci.</a> <a href="/?q=in%3A61319" title="Articles in this Issue">162, No. 1-2, 33-51 (1999)</a>. </div> <div class="abstract">Summary: We analyze an epidemiological model consisting of a linear chain of three cocirculating influenza $A$ strains that provide hosts exposed to a given strain with partial immune cross-protection against other strains. In the extreme case where infection with the middle strain prevents further infections from the other two strains, we reduce the model to a six-dimensional kernel capable of showing self-sustaining oscillations at relatively high levels of cross-protection. Dimensional reduction has been accomplished by a transformation of variables that preserves the eigenvalue responsible for the transition from damped oscillations to limit cycle solutions.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A1415866">Cited in <strong>33</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A92C60" title="MSC2020">92C60</a> </td> <td class="space"> Medical epidemiology </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A37N25" title="MSC2020">37N25</a> </td> <td class="space"> Dynamical systems in biology </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%3A37G15" title="MSC2020">37G15</a> </td> <td class="space"> Bifurcations of limit cycles and periodic orbits in dynamical systems </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Ainfluenza+drift">influenza drift</a>; <a href="/?q=ut%3Amultiple+strains">multiple strains</a>; <a href="/?q=ut%3Across-immunity">cross-immunity</a>; <a href="/?q=ut%3Asteady+states">steady states</a>; <a href="/?q=ut%3Adisease+free+equilibrium">disease free equilibrium</a>; <a href="/?q=ut%3Alimit+cycle">limit cycle</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 0947.92017" data-ciurl="/ci/01415866" data-biburl="/bibtex/01415866.bib" data-amsurl="/amsrefs/01415866.bib" data-xmlurl="/xml/01415866.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/01415866.pdf" title="Zbl 0947.92017 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/S0025-5564(99)00042-5" aria-label="DOI for “Dynamics of influenza A drift: The linear three-strain model”" title="10.1016/S0025-5564(99)00042-5">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">Gupta, S.; Ferguson, N.; Anderson, R., Chaos persistence and evolution of strain structure in antigenically diverse infectious agents, Science, 280, 912 (1998)</td> </tr><tr> <td>[2]</td> <td class="space">E.D. 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