Document Zbl 1430.92045

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A.</a>; <a href="/authors/shah.syed-wasim" title="Author Profile">Shah, Syed Wasim</a>; <a href="/authors/ullah.saif" title="Author Profile">Ullah, Saif</a>; <a href="/authors/gomez-aguilar.jose-francisco" title="Author Profile">Gómez-Aguilar, J. F.</a></div> <h2 class="title"> <strong>A dynamical model of asymptomatic carrier zika virus with optimal control strategies.</strong> <i>(English)</i> <a class="label nowrap" href="/1430.92045">Zbl 1430.92045</a> </h2> <div class="source"> <a href="/serials/2785" title="Journal Profile">Nonlinear Anal., Real World Appl.</a> <a href="/?q=in%3A444510" title="Articles in this Issue">50, 144-170 (2019)</a>. </div> <div class="abstract">Summary: A dynamical model of asymptomatic carrier zika virus model with optimal control strategies is presented. The basic model zika without control and basic mathematical results are obtained. The stability results for the zika model without controls are obtained when the basic reproduction number is less than unity at the disease free case. We show that the zika model without controls is locally and globally asymptotically stable when the basic reproduction number is less than 1. Further, we show the model stability at the endemic equilibrium and present that the model at the endemic equilibrium is locally and globally asymptotically stable when $\mathcal{R}_0 > 1$. Further, for the case when $\mathcal{R}_0 = 1$, we analyze the model and presents its backward bifurcation, and it may have the phenomena of backward bifurcation if the conditions provided is satisfied. After that we chose the appropriate controls for the zika virus eliminations and formulated the zika control model. These controls are the preventions through bednets, the treatment of the infected individuals due to zika virus infection, and the insecticides spraying on mosquitoes. With these controls, the model and the optimal controls characterizations are obtained. Furthermore, we provided the existence of optimal control problem. The model with controls and the model without controls are solved numerically by using backward Runge-Kutta method and obtain the graphical results. The graphical results are obtained by setting appropriate set of controls and the associated results are shown. We show that each strategy has its own importance for the elimination of zika virus infection, but we suggest based on the numerical results that the uses of bednets as a prevention from the zika mosquitoes, the treatment of individuals infected through zika mosquitoes and the insecticides spraying on mosquitoes could be more useful for the elimination of zika virus infection from the community. With this new idea of asymptotic carrier class the results provided in the present paper would be more useful for public health department and other health agencies to reduce the burden of zika virus infection from the community.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7155278">Cited in <strong>35</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%3A49N90" title="MSC2020">49N90</a> </td> <td class="space"> Applications of optimal control and differential games </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A34C23" title="MSC2020">34C23</a> </td> <td class="space"> Bifurcation theory for ordinary differential equations </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A34D23" title="MSC2020">34D23</a> </td> <td class="space"> Global stability of solutions to ordinary differential equations </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Azika+asymptomatic+carrier+model">zika asymptomatic carrier model</a>; <a href="/?q=ut%3Astability+results">stability results</a>; <a href="/?q=ut%3Abackward+bifurcation">backward bifurcation</a>; <a href="/?q=ut%3Aoptimal+controls">optimal controls</a>; <a href="/?q=ut%3Aoptimal+control+strategies">optimal control strategies</a>; <a href="/?q=ut%3Anumerical+results">numerical results</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 1430.92045" data-ciurl="/ci/07155278" data-biburl="/bibtex/07155278.bib" data-amsurl="/amsrefs/07155278.bib" data-xmlurl="/xml/07155278.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07155278.pdf" title="Zbl 1430.92045 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/j.nonrwa.2019.04.006" aria-label="DOI for “A dynamical model of asymptomatic carrier zika virus with optimal control strategies”" title="10.1016/j.nonrwa.2019.04.006">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">Simpson, D. 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