Novel stochastic dynamics of a fractal-fractional immune effector response to viral infection via latently infectious tissues

<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"> <html> <head> <meta name=renderer content=webkit> <meta http-equiv="X-UA-Compatible" content="IE=edge" /> <meta http-equiv="Content-Type" content="text/html; charset=utf-8" /> <meta name="viewport" content="width=device-width,initial-scale=1.0,maximum-scale=1.0,minimum-scale=1.0,user-scalable=no" /> <title>Novel stochastic dynamics of a fractal-fractional immune effector response to viral infection via latently infectious tissues</title> <meta name="_sowise_journalid" content="10001"/> <meta name="WT.cg_n" content="Mathematical Biosciences and Engineering"/> <meta name="prism.issn" content="1551-0018"/> <meta name="citation_issn" content="1551-0018"/> <meta name="journal_id" content="98"/> <meta name="dc.title" content="Novel stochastic dynamics of a fractal-fractional immune effector response to viral infection via latently infectious tissues"/> <meta name="dc.source" content="Mathematical Biosciences and Engineering 2022 11:11563"/> <meta name="dc.format" content="text/html"/> <meta name="dc.type" content="OriginalPaper"/> <meta name="prism.section" content="OriginalPaper"/> <meta name="prism.publicationName" content="Mathematical Biosciences and Engineering"/> <meta name="dc.date" content=""/> <meta name="dc.language" content="en"/> <meta name="dc.copyright" content="2022 The Author(s)"/> <meta name="dc.rightsAgent" content="mbe@aimspress.org"/> <meta name="prism.rightsAgent" content="mbe@aimspress.org"/> <meta name="dc.description" content="<abstract><p>In this paper, the global complexities of a stochastic virus transmission framework featuring adaptive response and Holling type II estimation are examined via the non-local fractal-fractional derivative operator in the Atangana-Baleanu perspective. Furthermore, we determine the existence-uniqueness of positivity of the appropriate solutions. Ergodicity and stationary distribution of non-negative solutions are carried out. Besides that, the infection progresses in the sense of randomization as a consequence of the response fluctuating within the predictive case's equilibria. Additionally, the extinction criteria have been established. To understand the reliability of the findings, simulation studies utilizing the fractal-fractional dynamics of the synthesized trajectory under the Atangana-Baleanu-Caputo derivative incorporating fractional-order $ \alpha $ and fractal-dimension $ \wp $ have also been addressed. The strength of white noise is significant in the treatment of viral pathogens. The persistence of a stationary distribution can be maintained by white noise of sufficient concentration, whereas the eradication of the infection is aided by white noise of high concentration.</p></abstract>"/> <meta name="og:description" content="In this paper, the global complexities of a stochastic virus transmission framework featuring adaptive response and Holling type II estimation are examined via the non-local fractal-fractional derivative operator in the Atangana-Baleanu perspective. Furthermore, we determine the existence-uniqueness of positivity of the appropriate solutions. Ergodicity and stationary distribution of non-negative solutions are carried out. Besides that, the infection progresses in the sense of randomization as a consequence of the response fluctuating within the predictive case's equilibria. Additionally, the extinction criteria have been established. To understand the reliability of the findings, simulation studies utilizing the fractal-fractional dynamics of the synthesized trajectory under the Atangana-Baleanu-Caputo derivative incorporating fractional-order $ \alpha $ and fractal-dimension $ \wp $ have also been addressed. The strength of white noise is significant in the treatment of viral pathogens. The persistence of a stationary distribution can be maintained by white noise of sufficient concentration, whereas the eradication of the infection is aided by white noise of high concentration."/> <meta name="description" content="<abstract><p>In this paper, the global complexities of a stochastic virus transmission framework featuring adaptive response and Holling type II estimation are examined via the non-local fractal-fractional derivative operator in the Atangana-Baleanu perspective. Furthermore, we determine the existence-uniqueness of positivity of the appropriate solutions. Ergodicity and stationary distribution of non-negative solutions are carried out. Besides that, the infection progresses in the sense of randomization as a consequence of the response fluctuating within the predictive case's equilibria. Additionally, the extinction criteria have been established. To understand the reliability of the findings, simulation studies utilizing the fractal-fractional dynamics of the synthesized trajectory under the Atangana-Baleanu-Caputo derivative incorporating fractional-order $ \alpha $ and fractal-dimension $ \wp $ have also been addressed. The strength of white noise is significant in the treatment of viral pathogens. The persistence of a stationary distribution can be maintained by white noise of sufficient concentration, whereas the eradication of the infection is aided by white noise of high concentration.</p></abstract>"/> <meta name="prism.publicationDate" content=""/> <meta name="prism.volume" content="19"/> <meta name="prism.number" content="mbe-19-11-539"/> <meta name="prism.startingPage" content="11563"/> <meta name="prism.endingPage" content="11594"/> <meta name="prism.copyright" content="2022 The Author(s)"/> <meta name="prism.url" content="http://www.aimspress.com/article/doi/10.3934/mbe.2022539"/> <meta name="prism.doi" content="doi:10.3934/mbe.2022539"/> <meta name="citation_pdf_url" content="http://www.aimspress.com/article/doi/10.3934/mbe.2022539"/> <meta name="citation_fulltext_html_url" content="http://www.aimspress.com/article/doi/10.3934/mbe.2022539"/> <meta name="citation_journal_title" content="Mathematical Biosciences and Engineering"/> <meta name="citation_journal_abbrev" content="MBE"/> <meta name="citation_title" content="Novel stochastic dynamics of a fractal-fractional immune effector response to viral infection via latently infectious tissues"/> <meta name="citation_volume" content="19"/> <meta name="citation_issue" content="11"/> <meta name="citation_online_date" content=""/> <meta name="citation_firstpage" content="11563"/> <meta name="citation_lastpage" content="11594"/> <meta name="citation_article_type" content="Article"/> <meta name="citation_fulltext_world_readable" content=""/> <meta name="citation_language" content="en"/> <meta name="dc.identifier" content="doi:10.3934/mbe.2022539"/> <meta name="DOI" content="10.3934/mbe.2022539"/> <meta name="citation_doi" content="10.3934/mbe.2022539"/> <meta name="dc.subject" content="Research article"/>  <meta name="dc.creator" content="Saima Rashid"/> <meta name="dc.creator" content="Rehana Ashraf"/> <meta name="dc.creator" content="Qurat-Ul-Ain Asif"/> <meta name="dc.creator" content="Fahd Jarad"/>  <meta name="citation_reference" content="S. 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style="position:relative;">  <div class="article-main-mid fl bgwhite gongshi"> <div class="clear"> <div class="article-journal fl" > <h3 class="journal-con" ><a href="/journal/mbe" class="journal-tit"> Mathematical Biosciences and Engineering </a></h3> <div class="article-list-time"> <font > 2022, <span><a href="/mbe/article/archives" class="mainColor">Volume 19</a>, </span> <a href="/mbe/article/2022/11/archive-articles" class="mainColor">Issue 11</a><span>:</span> <span>11563-11594</span>. </font> <font>doi: <a href="https://doi.org/10.3934/mbe.2022539" target="_blank" class="mainColor">10.3934/mbe.2022539</a></font> </div> </div> <div class="fr changebtn" > <a href="/article/doi/10.3934/mbe.2022538" class="page-btn prev-page fl">Previous Article</a> <a href="/article/doi/10.3934/mbe.2022540" class="page-btn next-page fl">Next Article</a> </div> </div> <div class="article-left"> <div class="article-column "> <span class="columnli">Research article</span> <span class="columnli access">Special Issues</span>   </div> <div class="articleEn"> <div class="article-title left-title"> <h1>Novel stochastic dynamics of a fractal-fractional immune effector response to viral infection via latently infectious tissues</h1> </div> <ul class="article-author clear"> <li > <a href="javascript:void(0);" class="mainColor" data-relate="saimarashid@gcuf.edu.pk" data="{{author.authorNameEn}}" type="authors.authorNameEn">Saima Rashid</a> <sup class="authorTag"> <a href="javascript:void(0);" class="com-num" data-tagVal="1">1</a> ,  <a href="javascript:void(0);" class="com-user" title="Corresponding Author: Saima Rashid, saimarashid@gcuf.edu.pk"></a>, <a href="mailto:saimarashid@gcuf.edu.pk" class="com-mail" title="mailto: saimarashid@gcuf.edu.pk"></a></sup>,  </li> <li > <a href="javascript:void(0);" class="mainColor" data-relate="" data="{{author.authorNameEn}}" type="authors.authorNameEn">Rehana Ashraf</a> <sup class="authorTag"> <a href="javascript:void(0);" class="com-num" data-tagVal="2">2</a> </sup>,  </li> <li > <a href="javascript:void(0);" class="mainColor" data-relate="" data="{{author.authorNameEn}}" type="authors.authorNameEn">Qurat-Ul-Ain Asif</a> <sup class="authorTag"> <a href="javascript:void(0);" class="com-num" data-tagVal="3">3</a> </sup>,  </li> <li > <a href="javascript:void(0);" class="mainColor" data-relate="fahd@cankaya.edu.tr" data="{{author.authorNameEn}}" type="authors.authorNameEn">Fahd Jarad</a> <sup class="authorTag"> <a href="javascript:void(0);" class="com-num" data-tagVal="4,5,6">4,5,6</a> ,  <a href="javascript:void(0);" class="com-user" title="Corresponding Author: Fahd Jarad, fahd@cankaya.edu.tr"></a>, <a href="mailto:fahd@cankaya.edu.tr" class="com-mail" title="mailto: fahd@cankaya.edu.tr"></a></sup> </li> </ul> <ul class="about-author">  <li class="article-author-address"> <span class=""> 1. </span> <div class="lostOf" > Department of Mathematics, Government College University, Faisalabad 38000, Pakistan </div> </li> <li class="article-author-address"> <span class=""> 2. </span> <div class="lostOf" > Department of Mathematics, Lahore College for Women University, Lahore, Pakistan </div> </li> <li class="article-author-address"> <span class=""> 3. </span> <div class="lostOf" > Department of Physics, Government College University, Faisalabad 38000, Pakistan </div> </li> <li class="article-author-address"> <span class=""> 4. </span> <div class="lostOf" > Department of Mathmatics, Cankaya University, Ankara, Turkey </div> </li> <li class="article-author-address"> <span class=""> 5. </span> <div class="lostOf" > Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan </div> </li> <li class="article-author-address"> <span class=""> 6. </span> <div class="lostOf" > Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia </div> </li> </br> <li class="article-author-address">Academic Editor: Xiang-Sheng Wang</li> </ul> <ul class="about-article">  <li class="com-author-info timewrap"> <span><b>Received:</b> 20 July 2022 </span> <span><b>Revised:</b> 31 July 2022 </span> <span><b>Accepted:</b> 02 August 2022 </span> <span><b>Published:</b> 12 August 2022 </span> </li> <li class="fundwrap"> </li> <li class="com-author-info"> </li> <li class="com-author-info"> <span class="columnli" id="article_special_show" hidden> </span> </li> </p> </li> </ul> </div> </div> <ul id="myTab" class="tab-ul tab-ul-article clear"> <li class="active abs"><a href="#Abstract" data-toggle="tab">Abstract</a></li> <li class="htm"><a href="#FullTextWrap" data-toggle="tab">Full Text(HTML)</a></li>  <li class="pdf hidden-sm hidden-xs"><div class="download-pdf" data="62f63f80ba35de77c348a0c6"><a href="javascript:void(0);" > Download PDF</a></div></li> <li class="pdf hidden-lg hidden-md"> <a href="/aimspress-data/mbe/2022/11/PDF/mbe-19-11-539.pdf" > Download PDF </a> </li> </ul> <ul class="article-tab-box tab-content" id="myTabContent">  <li id="Abstract" class="articleListBox tab-pane fade in active">   <div class="article-abstract"> <abstract><p>In this paper, the global complexities of a stochastic virus transmission framework featuring adaptive response and Holling type II estimation are examined via the non-local fractal-fractional derivative operator in the Atangana-Baleanu perspective. Furthermore, we determine the existence-uniqueness of positivity of the appropriate solutions. Ergodicity and stationary distribution of non-negative solutions are carried out. Besides that, the infection progresses in the sense of randomization as a consequence of the response fluctuating within the predictive case's equilibria. Additionally, the extinction criteria have been established. To understand the reliability of the findings, simulation studies utilizing the fractal-fractional dynamics of the synthesized trajectory under the Atangana-Baleanu-Caputo derivative incorporating fractional-order $ \alpha $ and fractal-dimension $ \wp $ have also been addressed. The strength of white noise is significant in the treatment of viral pathogens. The persistence of a stationary distribution can be maintained by white noise of sufficient concentration, whereas the eradication of the infection is aided by white noise of high concentration.</p></abstract> </div> <ul class="article-keyword article-info-en"> <b>Keywords:</b> <li><a class="underHigh mainColor" href="javascript:void(0);" data="immune effector response model" type="keywords.keywordEn">immune effector response model</a>, </li> <li><a class="underHigh mainColor" href="javascript:void(0);" data="fractal-fractional derivative operator" type="keywords.keywordEn">fractal-fractional derivative operator</a>, </li> <li><a class="underHigh mainColor" href="javascript:void(0);" data="Brownian motion" type="keywords.keywordEn">Brownian motion</a>, </li> <li><a class="underHigh mainColor" href="javascript:void(0);" data="ergodicity and stationary distribution" type="keywords.keywordEn">ergodicity and stationary distribution</a> </li> </ul> <p class="citation-p"><b class="subtit-b">Citation:</b> Saima Rashid, Rehana Ashraf, Qurat-Ul-Ain Asif, Fahd Jarad. Novel stochastic dynamics of a fractal-fractional immune effector response to viral infection via latently infectious tissues[J]. Mathematical Biosciences and Engineering, 2022, 19(11): 11563-11594. doi: 10.3934/mbe.2022539</p>  <div id="RelatedPages" class="articleListBox"> <h3><b class="subtit-b">Related Papers:</b></h3> <div id="RelatedPagesHtml"></div> </div> </li>  <li id="FullTextWrap" class="articleListBox FullText-all tab-pane fade in"> <h3 class="navTitle" id="Abstract-list">Abstract</h3>  <div class="article-abstract"> <abstract><p>In this paper, the global complexities of a stochastic virus transmission framework featuring adaptive response and Holling type II estimation are examined via the non-local fractal-fractional derivative operator in the Atangana-Baleanu perspective. Furthermore, we determine the existence-uniqueness of positivity of the appropriate solutions. Ergodicity and stationary distribution of non-negative solutions are carried out. Besides that, the infection progresses in the sense of randomization as a consequence of the response fluctuating within the predictive case's equilibria. Additionally, the extinction criteria have been established. To understand the reliability of the findings, simulation studies utilizing the fractal-fractional dynamics of the synthesized trajectory under the Atangana-Baleanu-Caputo derivative incorporating fractional-order $ \alpha $ and fractal-dimension $ \wp $ have also been addressed. The strength of white noise is significant in the treatment of viral pathogens. The persistence of a stationary distribution can be maintained by white noise of sufficient concentration, whereas the eradication of the infection is aided by white noise of high concentration.</p></abstract> </div> <br /> <div class="nodeTitle"><b></b></div> <br /> <div class="nodeContent"> </div> <div id="FullText" > <img style="display:block;margin:10px auto;" src="/style/web/images/article/1.gif" alt="加载中" /> </div>  </br>   </br> <h3 class="navTitle" id="References-list">References</h3> <div id="References"> <div class="References-wrap"> <table class="reference-tab"> <tr class="document-box" id="b1"> <td valign="top" class="td1"> [1] </td> <td class="td2">  S. Cassels, S. J. Clark, M. Morris, Mathematical models for HIV transmission dynamics, <i>J. Acquired Immune Defic. 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id="picsmall" class="picsmall clear"> </ul> </div> <a href="javascript:;" id="play_next" class="play_next"> <span class="imgShowIcon imgShowIcon-next"></span> </a> </div> </div> <ul id="miniImgs_title" hidden> <li> Figure 1. Life cycle of CD4+ and CD8+ T cells </li> <li> Figure 2. Aging and respiratory viral infection: from acute morbidity to chronic </li> <li> Figure 3. Graphical display of uninfected cells $ \mathbf{U}(\bar{\mathbf{t}}) $ and latently infected cells $ \mathbf{S}(\bar{\mathbf{t}}) $ of the model (5.1) considering the fractal-fractional derivative with generalized Mittag-Leffler kernel and varying fractional-order with fixed fractal-dimension </li> <li> Figure 4. Graphical display of actively infected cells $ \mathbf{A}(\bar{\mathbf{t}}) $ and free virus $ \mathbf{F}(\bar{\mathbf{t}}) $ of the model (5.1) considering the fractal-fractional derivative with generalized Mittag-Leffler kernel and varying fractional-order with fixed fractal-dimension </li> <li> Figure 5. Graphical display of antibodies $ \mathbf{Q}(\bar{\mathbf{t}}) $ of the model (5.1) considering the fractal-fractional derivative with generalized Mittag-Leffler kernel and varying fractional-order with fixed fractal-dimension </li> <li> Figure 6. Graphical display of uninfected cells $ \mathbf{U}(\bar{\mathbf{t}}) $ and latently infected cells $ \mathbf{S}(\bar{\mathbf{t}}) $ of the model (5.1) considering the fractal-fractional derivative with generalized Mittag-Leffler kernel and varying both fractional-order with fractal-dimension </li> <li> Figure 7. Graphical display of actively infected cells $ \mathbf{A}(\bar{\mathbf{t}}) $ and free virus $ \mathbf{F}(\bar{\mathbf{t}}) $ of the model (5.1) considering the fractal-fractional derivative with generalized Mittag-Leffler kernel and varying both fractional-order with fractal-dimension </li> <li> Figure 8. Graphical display of antibodies $ \mathbf{Q}(\bar{\mathbf{t}}) $ of the model (5.1) considering the fractal-fractional derivative with generalized Mittag-Leffler kernel and varying both fractional-order with fractal-dimension </li> <li> Figure 9. Graphical display of uninfected cells $ \mathbf{U}(\bar{\mathbf{t}}) $ and latently infected cells $ \mathbf{S}(\bar{\mathbf{t}}) $ of the model (5.1) considering the fractal-fractional derivative with generalized Mittag-Leffler kernel and varying fractal-dimension with fixed fractional-order </li> <li> Figure 10. Graphical display of actively infected cells $ \mathbf{A}(\bar{\mathbf{t}}) $ and free virus $ \mathbf{F}(\bar{\mathbf{t}}) $ of the model (5.1) considering the fractal-fractional derivative with generalized Mittag-Leffler kernel and varying fractal-dimension with fixed fractional-order </li> <li> Figure 11. Graphical display of antibodies $ \mathbf{Q}(\bar{\mathbf{t}}) $ of the model (5.1) considering the fractal-fractional derivative with generalized Mittag-Leffler kernel and varying fractal-dimension with fixed fractional-order </li> <li> Figure 12. Graphical display of uninfected cells $ \mathbf{U}(\bar{\mathbf{t}}) $ and latently infected cells $ \mathbf{S}(\bar{\mathbf{t}}) $ of the model (5.1) considering the fractal-fractional derivative with generalized Mittag-Leffler kernel and both varying fractal-dimension with fractional-order </li> <li> Figure 13. Graphical display of actively infected cells $ \mathbf{A}(\bar{\mathbf{t}}) $ and free virus $ \mathbf{F}(\bar{\mathbf{t}}) $ of the model (5.1) considering the fractal-fractional derivative with generalized Mittag-Leffler kernel and both varying fractal-dimension with fractional-order </li> <li> Figure 14. Graphical display of antibodies $ \mathbf{Q}(\bar{\mathbf{t}}) $ of the model (5.1) considering the fractal-fractional derivative with generalized Mittag-Leffler kernel and both varying fractal-dimension with fractional-order </li> <li> Figure 15. Graphical display of uninfected cells $ \mathbf{U}(\bar{\mathbf{t}}) $ and latently infected cells $ \mathbf{S}(\bar{\mathbf{t}}) $ of the model (5.1) with and without control when $ \alpha = 0.98 $ considering the fractal-fractional derivative with generalized Mittag-Leffler kernel </li> <li> Figure 16. Graphical display of actively infected cells $ \mathbf{A}(\bar{\mathbf{t}}) $ and free virus $ \mathbf{F}(\bar{\mathbf{t}}) $ of the model (5.1) with and without control when $ \alpha = 0.98 $ considering the fractal-fractional derivative with generalized Mittag-Leffler kernel </li> <li> Figure 17. Graphical display of antibodies $ \mathbf{Q}(\bar{\mathbf{t}}) $ of the model (5.1) with and without control when $ \alpha = 0.98 $ considering the fractal-fractional derivative with generalized Mittag-Leffler kernel </li> </ul> <div class="article-btn"> <div class="_table"> <div class="_cell"> <span></span> <span></span> <span></span> </div> </div> </div> <div class="article-menu"> <h3>Catalog</h3> <div class="article-menu-bot"> <ul class="iphone-wrapper"></ul> </div> </div> </body> 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Novel stochastic dynamics of a fractal-fractional immune effector response to viral infection via latently infectious tissues