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display:none; position:absolute; font-size:medium; font-weight: 700; text-align:center; color:White; width:75px; height:75px; top:0; left:25px; z-index:1"> <a href="/account/settings" id="ctl00_MainContent__home_AnnouncementHeader_photo_Edit" style=""><div style="padding-top:26px; color:White;">Edit</div></a> </div> <div id="ctl00_MainContent__home_AnnouncementHeader_photo_iconDiv" class="icons" style="text-decoration:none;"> <i id="ctl00_MainContent__home_AnnouncementHeader_photo_iconModerator" class="fa fa-certificate" title="MaplePrimes Moderator"></i> <img src="/images/leaf.png" id="ctl00_MainContent__home_AnnouncementHeader_photo_iconMaplesoft" title="Maplesoft Employee" /> </div> </div> </div> <div class="posttext pull-left" style="padding-bottom:0px;"> <h2><a id="ctl00_MainContent__home_AnnouncementHeader_title" href="/maplesoftblog/225643-Announcing-Maple-Flow-2024">Announcing Maple Flow 2024</a></h2> <span class="text-left"> by: <span id="ctl00_MainContent__home_AnnouncementHeader_memberLink_link" class="memberLink maplesoft"> <a id="ctl00_MainContent__home_AnnouncementHeader_memberLink_memberName" href="/users/Samir%20Khan">Samir Khan</a> <a id="ctl00_MainContent__home_AnnouncementHeader_memberLink_reputationLink" class="reputation" href="/users/Samir%20Khan/reputation">1894</a> </span></span> <label id="ctl00_MainContent__home_AnnouncementHeader_productLabel" style="padding-left:15px;"></label> <!-- display products here--> <label id="ctl00_MainContent__home_AnnouncementHeader_relatedProducts_productLabel">Product:</label> <a href="/products/Maple Flow/Maple Flow 2024"> Maple Flow 2024</a> <div class="time" style="text-align: left;"> <div class="tagList pull-left"> <div class="tagList"> <a href="/tags/engineering"> engineering</a> <a class="addNewTagLink" style="display:none">+ Manage Tags</a> </div> </div> </div> </div> <div class="clearfix"></div> </div> <div class="postinfo pull-right"> <div class="comments"> <div class="commentbg"> <span id="ctl00_MainContent__home_AnnouncementHeader_dateAsked">May 15 2024</span> <div class="mark"></div> </div> </div> <div class="views"><i class="fa fa-thumbs-up" style="color:rgba(108,160,194,1.00)"></i> 4 <i class="fa fa-comment" style="color:rgba(109,194,108,1.00)"></i> 0</div> </div> </div> </div> </div> <div class="postfull" style="height: 250px !important; overflow: hidden;"> <div id="ctl00_MainContent__home_announcementSummary" styles="padding: 10px !important;"> <span id="ctl00_MainContent__home_ann_summary"><p>We've just launched Maple Flow 2024!</p> <p>You're in the driving seat with Maple Flow - each new feature has a straight-line connection to a user-driven demand to work faster and more efficiently.</p> <p>Head on over <a href="https://www.maplesoft.com/products/Mapleflow/new-features/">here</a> for a rundown of everything that's new, but I thought I'd share my personal highlights here.</p> <p>If your result contains a large vector or matrix, you can now scroll to see more data. You can also change the size of the matrix to view more or fewer rows and columns.</p> <p><img src="/view.aspx?sf=225643_post/scrollable_matrix.gif"></p> <p>You can resize rows and columns if they're too large or small, and selectively enable row and column headers.</p> <p><img src="/view.aspx?sf=225643_post/scrollable_matrix_size.gif"></p> <p>If the vector or matrix in your result contains a unit, you can now rescale units with the Context Panel (for the entire matrix) or inline (for individual entries).</p> <p><img src="/view.aspx?sf=225643_post/change_units_in_matrix.gif"></p> <p>A few releases ago, we introduced the Variables palette to help you keep track of all the user-defined parameters at point of the grid cursor.</p> <p>You can now insert variables into the worksheet from the Variables palette. Just double-click on the appropriate name.</p> <p><img src="/view.aspx?sf=225643_post/Insert_variables_from_variables_palette.gif"></p> <p>Maple Flow already features command completion - just type the first few letters of a command, and a list of potential completions appears. Just pick the completion you need with a quick tap of the Tab key.</p> <p>We've supercharged this feature to give potential arguments for many popular functions. Type a function name followed by an opening bracket, and a list appears.</p> <p><img src="/view.aspx?sf=225643_post/Automatic_Argument_Completion.gif"></p> <p>In case you've missed it, the argument completion list also features (when they make sense) user-defined variables.</p> <p><img src="/view.aspx?sf=225643_post/fsolve_argument_completion.gif"></p> <p>You can now link to different parts of the same worksheet. This can be used to create a table of contents that lets you jump to different parts of larger worksheets.</p> <p><img src="/view.aspx?sf=225643_post/hyperlinks_and_bookmarks.gif"></p> <p><a href="https://www.maplesoft.com/products/Mapleflow/new-features/">This page </a>lists everything that's new in the current release, and all the prior releases. You might notice that we have three releases a year, each featuring many user-requested items. Let me know what you want to see next - you might not have to wait that long!</p> </span> </div> </div> <div class="row text-center top2footerBG top2footer" style="position: inherit; width: 100%; margin: 0;"> <a id="ctl00_MainContent__home_announcementLink" href="/maplesoftblog/225643-Announcing-Maple-Flow-2024">Read Full Post</a> </div> </div> </div> </div> <!-- Featured Posts Start --> <div id="ctl00_MainContent__home_pnlFeaturedPost"> <!-- Top 2 Posts --> <div id="topPosts"> <div class="sidebarblock" style="margin-bottom: 0px;"> <h3>Featured Post</h3> </div> <div class="post" style="height: 350px !important; overflow: hidden; position: relative;"> <div class="wrap-ut pull-left"> <div class="userinfo pull-left"> <div id="ctl00_MainContent__home_topPosts_ctrl0_photo_photoPanel" class="photo"> <a id="ctl00_MainContent__home_topPosts_ctrl0_photo_photoLink" href="/users/C_R"> <div class="avatar"> <img src="https://www.maplesoft.com/content/MemberPhotos/\651764_C_R_20230101074926.GIF" 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class="time"><span id="ctl00_MainContent__home_topPosts_ctrl0_photo_userReputation">2120</span></div> </div> </div> </div> <div class="posttext pull-left"> <div class="details"> <div class="upper"> <h3> <a href='/posts/225391-Interrupting-Maple--Evaluating-Forever'>Interrupting Maple –...</a></h3> </div> <div class="summary" style="overflow: auto"> <p><span style="font-size:16px;"><span style="font-family:"Times New Roman",serif"><span><span style="font-family:"Calibri",sans-serif">It can happen when an operation is interrupted by </span></span><img src="data:image/png;base64,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" style="width:35px; height:35px"><span><span style="font-family:"Calibri",sans-serif"> that Maple does not return to </span></span><img src="data:image/png;base64,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" style="width:81px; height:33px"><span style="font-family:"Calibri",sans-serif"> and still shows </span><img src="data:image/png;base64,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" style="width:126px; height:32px"><span><span style="font-family:"Calibri",sans-serif">. </span></span></span></span></p> <p><span style="font-size:16px;"><span style="font-family:"Times New Roman",serif"><span><span style="font-family:"Calibri",sans-serif">This can give the false impression that the Maple server in charge of the evaluation did not get the message to stop whatever it was doing.</span></span></span></span></p> <p><span style="font-size:16px;"><span style="font-family:"Times New Roman",serif"><span><span style="font-family:"Calibri",sans-serif">By giving Maple an impossible task to solve analytically</span></span></span></span></p> <pre class="prettyprint"> f1 := x1 - x1*sin(x1 + 5*x2) - x2*cos(5*x1 - x2); f2 := x2 - x2*sin(5*x1 - 3*x2) + x1*cos(3*x1 + 5*x2); solve({f1, f2});</pre> <p><span style="font-size:16px;"><span style="font-family:"Times New Roman",serif"><span><span style="font-family:"Calibri",sans-serif">I have noticed in the Windows Task Manager that freeing allocated memory can take much longer than one might think.</span></span></span></span></p> <p><span style="font-size:16px;"><span style="font-family:"Times New Roman",serif"><img src="data:image/png;base64,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" style="width:605px; height:30px"></span></span></p> <p><span style="font-size:16px;"><span style="font-family:"Times New Roman",serif"><span><span style="font-family:"Calibri",sans-serif">In one case it took 30 minutes to free 24 Gb of total allocated memory (21 Gb of it in RAM/physical memory). In this case the interrupt button became active (turned from grey </span></span></span></span><img src="data:image/png;base64,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"><span style="font-size:16px;"><span style="font-family:"Times New Roman",serif"><span><span style="font-family:"Calibri",sans-serif"> to red </span></span><img src="data:image/png;base64,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" style="width:35px; height:35px"><span><span style="font-family:"Calibri",sans-serif">) two times and memory continued piling up again.</span></span></span></span></p> <p><span style="font-size:16px;"><span style="font-family:"Times New Roman",serif"><span><span style="font-family:"Calibri",sans-serif">Lessons learned for me:</span></span></span></span></p> <ul> <li><span style="font-size:16px;"><span style="font-family:"Times New Roman",serif"><span><span style="font-family:"Calibri",sans-serif">The task manager is not only a valuable indicator for task activity but also for the interruption/memory freeing process.</span></span></span></span></li> <li><span style="font-size:16px;"><span style="font-family:"Times New Roman",serif"><span><span style="font-family:"Calibri",sans-serif">Before killing a whole Maple session and potentially losing the last state of a worksheet it can pay off to wait and repeatedly interrupt an operation.</span></span></span></span></li> </ul> <p> </p> <p><span style="font-size:16px;"><span style="font-family:"Times New Roman",serif"><span><span style="font-family:"Calibri",sans-serif">Suggestion: When the maple server gets an interrupt request, it could report to the GUI that it is in an interruption state and is no longer evaluating input. For example changing the message in the status bar from Evaluating... to Interrupting... </span></span></span></span></p> </div> </div> </div> <div class="clearfix"> </div> </div> <div class="postinfo pull-left"> <div class="comments"> <div class="commentbg"> April 28 <div class="mark"> </div> </div> </div> <div class="views"> <i class="fa fa-thumbs-up" style="color: rgba(108,160,194,1.00)"></i> 9 <i class="fa fa-comment" style="color: rgba(109,194,108,1.00)"></i> 3 </div> <div class="time"> <div class="tagList"> <div class="tagList"> <a href="/tags/interrupt"> interrupt</a> <a href="/tags/gui"> gui</a> <a class="addNewTagLink" style="display:none">+ Manage Tags</a> </div> </div> </div> </div> <div class="clearfix"> </div> <div class="row text-center top2footerBG top2footer"><a href='/posts/225391-Interrupting-Maple--Evaluating-Forever'>Read Full Post</a></div> </div> <div class="sidebarblock" style="margin-bottom: 0px;"> <h3>Featured Post</h3> </div> <div class="post" style="height: 350px !important; overflow: hidden; position: relative;"> <div class="wrap-ut pull-left"> <div class="userinfo pull-left"> <div id="ctl00_MainContent__home_topPosts_ctrl1_photo_photoPanel" class="photo"> <a id="ctl00_MainContent__home_topPosts_ctrl1_photo_photoLink" href="/users/Paras31"> <div class="avatar"> <img src="https://www.maplesoft.com/content/MemberPhotos/\4065368_Paras31_20240422174152.jpeg" id="ctl00_MainContent__home_topPosts_ctrl1_photo_memberPhoto" width="75" height="75" /> </div> </a> <div id="editImage" style="background:rgba(0, 0, 0, .6) 70%; display:none; position:absolute; font-size:medium; font-weight: 700; text-align:center; color:White; width:75px; height:75px; top:0; left:25px; z-index:1"> <a href="/account/settings" id="ctl00_MainContent__home_topPosts_ctrl1_photo_Edit" style=""><div style="padding-top:26px; color:White;">Edit</div></a> </div> <div id="ctl00_MainContent__home_topPosts_ctrl1_photo_nameDiv" class="icons"> <div class="views"><a href="/users/Paras31" id="ctl00_MainContent__home_topPosts_ctrl1_photo_memberName"><span id="ctl00_MainContent__home_topPosts_ctrl1_photo_userName">Paras31</span></a></div> <div class="time"><span id="ctl00_MainContent__home_topPosts_ctrl1_photo_userReputation">25</span></div> </div> </div> </div> <div class="posttext pull-left"> <div class="details"> <div class="upper"> <h3> <a href='/posts/225528-Exploring-The-SIR-Model-With-Vaccination'>Exploring the SIR Model...</a></h3> </div> <div class="summary" style="overflow: auto"> <p>In our recent project, we're diving deep into understanding the SIR model—a fundamental framework in epidemiology that helps us analyze how diseases spread through populations. The SIR model categorizes individuals into three groups: <strong>Susceptible (S)</strong>, <strong>Infected (I)</strong>, and <strong>Recovered (R)</strong>. By tracking how people move through these categories, we can predict disease dynamics and evaluate interventions.</p> <p><strong>Key Points of the SIR Model:</strong></p> <ul> <li><strong>Susceptible (S):</strong> Individuals who can catch the disease.</li> <li><strong>Infected (I):</strong> Those currently infected and capable of spreading the disease.</li> <li><strong>Recovered (R):</strong> Individuals who have recovered and developed immunity.</li> </ul> <p><strong>Vaccination Impact:</strong> One of the critical interventions in disease control is vaccination, which moves individuals directly from the susceptible to the recovered group. This simple action reduces the number of people at risk, thereby lowering the overall spread of the disease.</p> <p>We're experimenting with a simple model to understand how different vaccination rates can significantly alter the dynamics of an outbreak. By simulating scenarios with varying vaccination coverage, students can observe how herd immunity plays a crucial role in controlling diseases. Our goal is to make these abstract concepts clear and relatable through practical modeling exercises.</p> <form name="worksheet_form"> <table align="center" width="768"> <tbody> <tr> <td> <p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"><br> </p> <input name="md.ref" type="hidden" value="3F36FF5B3B5627886CD31DC4B1DB89D7"> <table align="center" width="768"> <tbody> <tr> <td> <p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"><span style="color:#000000;font-size: 100%;font-family: Times New Roman,serif;font-weight:normal;font-style:normal;">In this exercise, we are going back to the simple SIR model, without births or deaths, to look at the effect of vaccination. The aim of this activity is to represent vaccination in a very simple way - we are assuming it already happened before we run our model! By changing the initial conditions, we can prepare the population so that it has received a certain coverage of vaccination.</span><br> <span style="color:#000000;font-size: 100%;font-family: Times New Roman,serif;font-weight:normal;font-style:normal;"></span><br> <span style="color:#000000;font-size: 100%;font-family: Times New Roman,serif;font-weight:normal;font-style:normal;">We are starting with the transmission and recovery parameters </span><img alt="b = .4/days" height="27" src="/ViewTemp.ashx?f=4065368_1715086171/10b7704c9449348a300f4404ee84b713.gif" style="vertical-align:-6px" width="91"><span style="color:#000000;font-size: 100%;font-family: Times New Roman,serif;font-weight:normal;font-style:normal;">and </span><img alt="c = .1/days" height="27" src="/ViewTemp.ashx?f=4065368_1715086171/38695221cd7387896081017366d3eae3.gif" style="vertical-align:-6px" width="90"><span style="color:#000000;font-size: 100%;font-family: Times New Roman,serif;font-weight:normal;font-style:normal;"> . To incorporate immunity from vaccination in the model, we assume that a proportion p of the total population starts in the recovered compartment, representing the vaccine coverage and assuming the vaccine is perfectly effective. Again, we assume the epidemic starts with a single infected case introduced into the population.</span><br> <span style="color:#000000;font-size: 100%;font-family: Times New Roman,serif;font-weight:normal;font-style:normal;">We are going to model this scenario for a duration of 2 years, assuming that the vaccine coverage is 50%, and plot the prevalence in each compartment over time.</span></p> <p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"><span style="color:#000000;font-size: 100%;font-family: Times New Roman,serif;font-weight:normal;font-style:normal;"> </span></p> <p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"><img align="middle" alt="restart" height="41" src="/ViewTemp.ashx?f=4065368_1715086171/603c4423640b9c2f5a5a3fee00133a40.gif" style="vertical-align:-24px" width="768"><br> <img alt="with(plots)" height="23" src="/ViewTemp.ashx?f=4065368_1715086171/5cfb6200ea37c2e95ac5f2dd68037b9d.gif" style="vertical-align:-6px" width="87"></p> <p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"><img alt="b := .4; c := .1; n := 10^6; p := .5" height="23" src="/ViewTemp.ashx?f=4065368_1715086171/7e6d23b1553e305d280056f8e0bd88cd.gif" style="vertical-align:-6px" width="259"></p> <p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"><img align="middle" alt="deS := diff(S(t), t) = -b*S(t)*I0(t); deI := diff(I0(t), t) = b*S(t)*I0(t)-c*I0(t); deR := diff(R(t), t) = c*I0(t)" height="59" src="/ViewTemp.ashx?f=4065368_1715086171/215897707516d0f520a7a73845376269.gif" style="vertical-align:-42px" width="768"></p> <table> <tbody> <tr valign="baseline"> <td> <p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"><img alt="diff(R(t), t) = .1*I0(t)" height="42" src="/ViewTemp.ashx?f=4065368_1715086171/a1b90f4e8f1df5a5a8289f2b910b0592.gif" style="vertical-align:-16px" width="175"></p> </td> <td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;">(1)</td> </tr> </tbody> </table> <p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"><img align="middle" alt="F := dsolve([deS, deI, deR, S(0) = 1-p, I0(0) = 1/n, R(0) = p], [S(t), I0(t), R(t)], numeric, method = rkf45, maxfun = 100000)" height="60" src="/ViewTemp.ashx?f=4065368_1715086171/bb62cf651b0d15960b0760855d5fafef.gif" style="vertical-align:-43px" width="768"></p> <p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"><img align="middle" alt="odeplot(F, [[t, S(t)], [t, I0(t)], [t, R(t)]], t = 0 .. 730, colour = [blue, red, green], legend = ["S(t)", "I0(t)", "R(t)"], labels = ["Time (days)", " Proportion\nof Population "], title = "SIR Model with vaccine coverage 50 %", size = [500, 300])" height="78" src="/ViewTemp.ashx?f=4065368_1715086171/5fcd361697397080a89b97e1256cca90.gif" style="vertical-align:-61px" width="768"></p> <table> <tbody> <tr valign="baseline"> <td> <p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"><img align="middle" height="300" src="/ViewTemp.ashx?f=4065368_1715086171/fd044f4c3265bdab03204be826567ec7.gif" style="border:none" width="500"></p> </td> <td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"> </td> </tr> </tbody> </table> <p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"><img alt="F(100)" height="23" src="/ViewTemp.ashx?f=4065368_1715086171/96b22a72b1c9687cddbb890e10903a8d.gif" style="vertical-align:-6px" width="62"></p> <table> <tbody> <tr valign="baseline"> <td> <p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"><img alt="[t = 100., S(t) = HFloat(0.46146837378273076), I0(t) = HFloat(0.018483974421123688), R(t) = HFloat(0.5200486517961457)]" height="23" src="/ViewTemp.ashx?f=4065368_1715086171/dd4f4b385a71564d7d6589a1b0419995.gif" style="vertical-align:-6px" width="593"></p> </td> <td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;">(2)</td> </tr> </tbody> </table> <p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"><img alt="eval(S(:-t), F(100))" height="23" src="/ViewTemp.ashx?f=4065368_1715086171/a8b1c6815d462e0b584a8bf542a2cabb.gif" style="vertical-align:-6px" width="133"></p> <table> <tbody> <tr valign="baseline"> <td> <p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"><img alt="HFloat(0.46146837378273076)" height="23" src="/ViewTemp.ashx?f=4065368_1715086171/717363ab8bd250ff705b840b900be2fd.gif" style="vertical-align:-6px" width="129"></p> </td> <td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;">(3)</td> </tr> </tbody> </table> <p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"><img align="middle" alt="Reff := proc (s) options operator, arrow; b*(eval(S(:-t), F(s)))/(c*n) end proc; Reff(100)" height="41" src="/ViewTemp.ashx?f=4065368_1715086171/c22c20ee36cd398eb906e445ac26f3e1.gif" style="vertical-align:-24px" width="768"></p> <table> <tbody> <tr valign="baseline"> <td> <p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"><img alt="HFloat(1.845873495130923e-6)" height="25" src="/ViewTemp.ashx?f=4065368_1715086171/90f4344cd0a8d0016079265865fd748f.gif" style="vertical-align:-6px" width="171"></p> </td> <td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;">(4)</td> </tr> </tbody> </table> <p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"><img alt="plot(Reff, 0 .. 730, size = [500, 300])" height="6" src="/ViewTemp.ashx?f=4065368_1715086171/9fc1be11dbb7485bfc3f8c481496be09.gif" style="vertical-align:-6px" width="768"></p> <table> <tbody> <tr valign="baseline"> <td> <p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"><img align="middle" height="300" src="/ViewTemp.ashx?f=4065368_1715086171/cb99149f86c70eeff9d1ee65c5b7e0d2.gif" style="border:none" width="500"></p> </td> <td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"> </td> </tr> </tbody> </table> <p align="left" style="margin:0 0 0 0; padding-top:8px; padding-bottom:4px"><span style="color:#ff0000;font-size: 150%;font-family: Times New Roman,serif;font-weight:bold;font-style:normal;">Increasing the vaccine coverage to 75%</span></p> <p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"><img alt="NULL" height="23" src="/ViewTemp.ashx?f=4065368_1715086171/3544960b7ecae790e58bc4ca3442a159.gif" style="vertical-align:-6px" width="9"></p> <p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"><img align="middle" alt="restart" height="41" src="/ViewTemp.ashx?f=4065368_1715086171/754f90bd82ca78996ebba2ad1df6ea6d.gif" style="vertical-align:-24px" width="768"><br> <img alt="with(plots)" height="23" src="/ViewTemp.ashx?f=4065368_1715086171/98f256e7c67319ad6f88290daa8aa4bd.gif" style="vertical-align:-6px" width="87"></p> <p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"><img alt="b := .4; c := .1; n := 10^6; p := .75" height="23" src="/ViewTemp.ashx?f=4065368_1715086171/1c7a5370e5686dbca9f9a8d683c1c634.gif" style="vertical-align:-6px" width="270"></p> <p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"><img align="middle" alt="deS := diff(S(t), t) = -b*S(t)*I0(t); deI := diff(I0(t), t) = b*S(t)*I0(t)-c*I0(t); deR := diff(R(t), t) = c*I0(t)" height="59" src="/ViewTemp.ashx?f=4065368_1715086171/215ddd2a764c8a88bfa1d9bebc07e8f5.gif" style="vertical-align:-42px" width="768"></p> <table> <tbody> <tr valign="baseline"> <td> <p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"><img alt="diff(R(t), t) = .1*I0(t)" height="42" src="/ViewTemp.ashx?f=4065368_1715086171/7826ec0ae1ae1a98fbd8225b28ebf224.gif" style="vertical-align:-16px" width="175"></p> </td> <td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;">(5)</td> </tr> </tbody> </table> <p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"><img alt="NULL" height="23" src="/ViewTemp.ashx?f=4065368_1715086171/3faa437923a950daf57391dcf74b3529.gif" style="vertical-align:-6px" width="9"></p> <p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"><img align="middle" alt="F1 := dsolve([deS, deI, deR, S(0) = 1-p, I0(0) = 1/n, R(0) = p], [S(t), I0(t), R(t)], numeric, method = rkf45, maxfun = 100000)" height="60" src="/ViewTemp.ashx?f=4065368_1715086171/5b619ea17bf17ed64bf9f853136e9553.gif" style="vertical-align:-43px" width="768"></p> <p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"><img align="middle" alt="odeplot(F1, [[t, S(t)], [t, I0(t)], [t, R(t)]], t = 0 .. 730, colour = [blue, red, green], legend = ["S(t)", "I0(t)", "R(t)"], labels = ["Time (days)", " Proportion\nof Population "], title = "SIR Model with vaccine coverage 75%", size = [500, 300])" height="78" src="/ViewTemp.ashx?f=4065368_1715086171/f4ed8f22bdf3f78061994e33f65caea0.gif" style="vertical-align:-61px" width="768"></p> <table> <tbody> <tr valign="baseline"> <td> <p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"><img align="middle" height="300" src="/ViewTemp.ashx?f=4065368_1715086171/92b161e04704d08fff480fbb2cc05014.gif" style="border:none" width="500"></p> </td> <td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"> </td> </tr> </tbody> </table> <p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"><img alt="F(1100)" height="23" src="/ViewTemp.ashx?f=4065368_1715086171/c858b3bd3ff97937055710890b2a5f76.gif" style="vertical-align:-6px" width="73"></p> <p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"><img alt="eval(S(:-t), F1(100))" height="23" src="/ViewTemp.ashx?f=4065368_1715086171/a242d8f5792ea0e5ed6f7f11e1678a79.gif" style="vertical-align:-6px" width="140"></p> <table> <tbody> <tr valign="baseline"> <td> <p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"><img alt="HFloat(0.249990000844159)" height="23" src="/ViewTemp.ashx?f=4065368_1715086171/6bab395f89e8874533ce3d6fd7f4ba4a.gif" style="vertical-align:-6px" width="129"></p> </td> <td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;">(6)</td> </tr> </tbody> </table> <p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"><img align="middle" alt="Reff := proc (s) options operator, arrow; b*(eval(S(:-t), F1(s)))/(c*n) end proc; Reff(100)" height="41" src="/ViewTemp.ashx?f=4065368_1715086171/8293c33ebb71d843f42cb6fac784f8b1.gif" style="vertical-align:-24px" width="768"></p> <table> <tbody> <tr valign="baseline"> <td> <p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"><img alt="HFloat(9.99960003376636e-7)" height="25" src="/ViewTemp.ashx?f=4065368_1715086171/1321de9c67513972a68ae59f72faeae7.gif" style="vertical-align:-6px" width="171"></p> </td> <td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;">(7)</td> </tr> </tbody> </table> <p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"><img alt="plot(Reff, 0 .. 730, size = [500, 300])" height="6" src="/ViewTemp.ashx?f=4065368_1715086171/d34bf093abbe78899e18e149365d1d68.gif" style="vertical-align:-6px" width="768"></p> <table> <tbody> <tr valign="baseline"> <td> <p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"><img align="middle" height="300" src="/ViewTemp.ashx?f=4065368_1715086171/f0473f68d0246f5fd3927071a1a3834f.gif" style="border:none" width="500"></p> </td> <td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"> </td> </tr> </tbody> </table> <p align="left" style="margin:0 0 0 0; padding-top:8px; padding-bottom:4px"><span style="color:#ff0000;font-size: 150%;font-family: Times New Roman,serif;font-weight:bold;font-style:normal;">Does everyone in the population need to be vaccinated in order to prevent an epidemic?What do you observe if you model the infection dynamics with different values for p?</span></p> <p align="left" style="margin:0 0 0 0; padding-top:8px; padding-bottom:4px"><span style="color:#000000;font-size: 100%;font-family: Times New Roman,serif;font-weight:normal;font-style:normal;">No, not everyone in the population needs to be vaccinated in order to prevent an epidemic . In this scenario, if p equals 0.75 or higher, no epidemic occurs - 75 % is the critical vaccination/herd immunity threshold . Remember,, herd immunity describes the phenomenon in which there is sufficient immunity in a population to interrupt transmission . Because of this, not everyone needs to be vaccinated to prevent an outbreak .</span></p> <p align="left" style="margin:0 0 0 0; padding-top:8px; padding-bottom:4px"><span style="color:#ff0000;font-size: 150%;font-family: Times New Roman,serif;font-weight:bold;font-style:normal;">What proportion of the population needs to be vaccinated in order to prevent an epidemic if </span><img alt="b = .4" height="33" src="/ViewTemp.ashx?f=4065368_1715086171/82ff1e76e2c60ac4a8d7e910fcf055f4.gif" style="vertical-align:-8px" width="78"><span style="color:#ff0000;font-size: 150%;font-family: Times New Roman,serif;font-weight:normal;font-style:normal;">and </span><img alt="c = .2/days" height="46" src="/ViewTemp.ashx?f=4065368_1715086171/6386d4708b41f42afbcfdee72a805657.gif" style="vertical-align:-8px" width="142"><span style="color:#ff0000;font-size: 150%;font-family: Times New Roman,serif;font-weight:normal;font-style:normal;">? What if </span><img alt="b = .6" height="33" src="/ViewTemp.ashx?f=4065368_1715086171/21e9ca1ea5df69afdc2557f7fa2123ff.gif" style="vertical-align:-8px" width="69"><span style="color:#ff0000;font-size: 150%;font-family: Times New Roman,serif;font-weight:normal;font-style:normal;"> and </span><img alt=""c=0.1 days^(-1)?"" height="46" src="/ViewTemp.ashx?f=4065368_1715086171/29908a8eeafced78040f198ee5f98db8.gif" style="vertical-align:-8px" width="151"></p> <p align="left" style="margin:0 0 0 0; padding-top:8px; padding-bottom:4px"><span style="color:#000000;font-size: 100%;font-family: Times New Roman,serif;font-weight:normal;font-style:normal;">In the context of the SIR model, the critical proportion of the population that needs to be vaccinated in order to prevent an epidemic is often referred to as the "herd immunity threshold" or "critical vaccination coverage."</span></p> <table style="margin-left:0px;margin-right:0px"> <tbody> <tr valign="baseline"> <td><span style="color:#000000;font-size: 100%;font-family: Times New Roman,serif;font-weight:normal;font-style:normal;">• </span></td> <td> <p align="left" style="margin:0 0 0 0; padding-top:3px; padding-bottom:3px"><span style="color:#000000;font-size: 100%;font-family: Times New Roman,serif;font-weight:bold;font-style:normal;">Scenario 1:</span><span style="color:#000000;font-size: 100%;font-family: Times New Roman,serif;font-weight:normal;font-style:normal;"> </span><img alt="b = .4" height="23" src="/ViewTemp.ashx?f=4065368_1715086171/06450aa43093a64f6726f2383a31b70c.gif" style="vertical-align:-6px" width="50"><span style="color:#000000;font-size: 100%;font-family: Times New Roman,serif;font-weight:normal;font-style:normal;">and </span><img alt="c = .2/days" height="27" src="/ViewTemp.ashx?f=4065368_1715086171/e304b164c68093e7cab7a2e8893c2a4e.gif" style="vertical-align:-6px" width="90"><br> <img align="middle" height="40" src="/ViewTemp.ashx?f=4065368_1715086171/7c9f6f438f7d975e856fcb7479e8db39.gif" style="vertical-align:-23px" width="600"><br> <img alt="``" height="23" src="/ViewTemp.ashx?f=4065368_1715086171/3e35d2a6920fe27dcb1b3f1bd640f72a.gif" style="vertical-align:-6px" width="11"></p> </td> </tr> </tbody> </table> <p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"><img align="middle" alt="restart" height="41" src="/ViewTemp.ashx?f=4065368_1715086171/e3d2a1ff7ae84a200c85eeaa1f9956ee.gif" style="vertical-align:-24px" width="768"><br> <img alt="with(plots)" height="23" src="/ViewTemp.ashx?f=4065368_1715086171/7d59568fd5c2b80f6aec6e2f88a5e738.gif" style="vertical-align:-6px" width="87"></p> <p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"><img alt="b := .4; c := .2; n := 10^6; p := .5" height="23" src="/ViewTemp.ashx?f=4065368_1715086171/51607858102e98ad67b22e674f9e81fc.gif" style="vertical-align:-6px" width="259"><img alt="``" height="23" src="/ViewTemp.ashx?f=4065368_1715086171/f3bb933b18ba41dd65dda0f97cea90b6.gif" style="vertical-align:-6px" width="11"></p> <p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"><img align="middle" alt="deS := diff(S(t), t) = -b*S(t)*I0(t); deI := diff(I0(t), t) = b*S(t)*I0(t)-c*I0(t); deR := diff(R(t), t) = c*I0(t)" height="59" src="/ViewTemp.ashx?f=4065368_1715086171/9a458e77dce925da5b8a2a9a69bfb365.gif" style="vertical-align:-42px" width="768"></p> <table> <tbody> <tr valign="baseline"> <td> <p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"><img alt="diff(R(t), t) = .2*I0(t)" height="42" src="/ViewTemp.ashx?f=4065368_1715086171/6ec4056a1b6005b64967d1f408488afa.gif" style="vertical-align:-16px" width="175"></p> </td> <td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;">(8)</td> </tr> </tbody> </table> <p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"><img align="middle" alt="F1 := dsolve([deS, deI, deR, S(0) = 1-p, I0(0) = 1/n, R(0) = p], [S(t), I0(t), R(t)], numeric, method = rkf45, maxfun = 100000)" height="60" src="/ViewTemp.ashx?f=4065368_1715086171/c75a6ac3880d28c53783591b9e503230.gif" style="vertical-align:-43px" width="768"></p> <p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"><img alt="odeplot(F1, [[t, S(t)], [t, I0(t)], [t, R(t)]], t = 0 .. 730, colour = [blue, red, green], legend = ["S(t)", "I0(t)", "R(t)"], labels = ["Time (days)", " Proportion\nof Population "], title = "SIR Model with vaccine coverage 50 %", size = [500, 300])" height="6" src="/ViewTemp.ashx?f=4065368_1715086171/f81a053cc39f86e78c963b97d40d2db2.gif" style="vertical-align:-6px" width="768"></p> <table> <tbody> <tr valign="baseline"> <td> <p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"><img align="middle" height="300" src="/ViewTemp.ashx?f=4065368_1715086171/d09666048b0468b3c0d98084ca83f447.gif" style="border:none" width="500"></p> </td> <td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"> </td> </tr> </tbody> </table> <p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"><br> <span style="color:#000000;font-size: 100%;font-family: Times New Roman,serif;font-weight:normal;font-style:normal;">The required vaccination coverage is around 50% .</span></p> <table style="margin-left:0px;margin-right:0px"> <tbody> <tr valign="baseline"> <td><span style="color:#000000;font-size: 100%;font-family: Times New Roman,serif;font-weight:normal;font-style:normal;">• </span></td> <td> <p align="left" style="margin:0 0 0 0; padding-top:3px; padding-bottom:3px"><span style="color:#000000;font-size: 100%;font-family: Times New Roman,serif;font-weight:bold;font-style:normal;">Scenario 1:</span><span style="color:#000000;font-size: 100%;font-family: Times New Roman,serif;font-weight:normal;font-style:normal;"> </span><img alt="b = .6" height="23" src="/ViewTemp.ashx?f=4065368_1715086171/74f400b29ebab2234d44fec97b517565.gif" style="vertical-align:-6px" width="50"><span style="color:#000000;font-size: 100%;font-family: Times New Roman,serif;font-weight:normal;font-style:normal;">and </span><img alt="c = .1/days" height="27" src="/ViewTemp.ashx?f=4065368_1715086171/d4b1f1eab5a684c6ccfe5b0fe9cb79ad.gif" style="vertical-align:-6px" width="90"></p> </td> </tr> </tbody> </table> <p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"><img align="middle" alt="restart" height="41" src="/ViewTemp.ashx?f=4065368_1715086171/5930790690b668b3bf71f7d8a9f3c4ef.gif" style="vertical-align:-24px" width="768"><br> <img alt="with(plots)" height="23" src="/ViewTemp.ashx?f=4065368_1715086171/ccb8b74b3591e29f8cafd257d99a8a71.gif" style="vertical-align:-6px" width="87"></p> <p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"><img alt="b := .6; c := .1; n := 10^6; p := .83" height="23" src="/ViewTemp.ashx?f=4065368_1715086171/c5b85c9d5dab63748ba4b0948261a268.gif" style="vertical-align:-6px" width="267"><img alt="NULL" height="23" src="/ViewTemp.ashx?f=4065368_1715086171/dee6080122ad01db8265a56a46940658.gif" style="vertical-align:-6px" width="11"></p> <p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"><img align="middle" alt="deS := diff(S(t), t) = -b*S(t)*I0(t); deI := diff(I0(t), t) = b*S(t)*I0(t)-c*I0(t); deR := diff(R(t), t) = c*I0(t)" height="59" src="/ViewTemp.ashx?f=4065368_1715086171/dc22d32d17999d10b58dbecaf7136b32.gif" style="vertical-align:-42px" width="768"></p> <table> <tbody> <tr valign="baseline"> <td> <p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"><img alt="diff(R(t), t) = .1*I0(t)" height="42" src="/ViewTemp.ashx?f=4065368_1715086171/ee21aa6534a6023a9422b0748b55226c.gif" style="vertical-align:-16px" width="175"></p> </td> <td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;">(9)</td> </tr> </tbody> </table> <p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"><img alt="NULL" height="23" src="/ViewTemp.ashx?f=4065368_1715086171/898f746449741b886cf588f96b7641e8.gif" style="vertical-align:-6px" width="9"></p> <p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"><img align="middle" alt="F1 := dsolve([deS, deI, deR, S(0) = 1-p, I0(0) = 1/n, R(0) = p], [S(t), I0(t), R(t)], numeric, method = rkf45, maxfun = 100000)" height="60" src="/ViewTemp.ashx?f=4065368_1715086171/f77cf54f60ca2be78b6377c581a8e79c.gif" style="vertical-align:-43px" width="768"></p> <p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"><img alt="odeplot(F1, [[t, S(t)], [t, I0(t)], [t, R(t)]], t = 0 .. 730, colour = [blue, red, green], legend = ["S(t)", "I0(t)", "R(t)"], labels = ["Time (days)", " Proportion\nof Population "], title = "SIR Model with vaccine coverage 83% ", size = [500, 300])" height="6" src="/ViewTemp.ashx?f=4065368_1715086171/b6adfa27befe03121b351993a9630e75.gif" style="vertical-align:-6px" width="768"></p> <table> <tbody> <tr valign="baseline"> <td> <p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"><img align="middle" height="300" src="/ViewTemp.ashx?f=4065368_1715086171/40b3c9b31642d57f403ed3b8bb44a4ea.gif" style="border:none" width="500"></p> </td> <td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"> </td> </tr> </tbody> </table> <p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"><img alt=""The required vaccination coverage is around 83 `%` ."" height="23" src="/ViewTemp.ashx?f=4065368_1715086171/9895560c5ae19a7bca43a0e58b604c48.gif" style="vertical-align:-6px" width="309"></p> </td> </tr> </tbody> </table> <input name="sequence" type="hidden" value="1"> <input name="cmd" type="hidden" value="none"> <p><br> <a href="/ViewTemp.ashx?f=4065368_1715086171/SIR_simple_vaccination_example.mw">Download SIR_simple_vaccination_example.mw</a></p> </td> </tr> </tbody> </table> </form> </div> </div> </div> <div class="clearfix"> </div> </div> <div class="postinfo pull-left"> <div class="comments"> <div class="commentbg"> May 07 <div class="mark"> </div> </div> </div> <div class="views"> <i class="fa fa-thumbs-up" style="color: rgba(108,160,194,1.00)"></i> 0 <i class="fa fa-comment" style="color: rgba(109,194,108,1.00)"></i> 2 </div> <div class="time"> <div class="tagList"> <div class="tagList"> <a href="/tags/ode"> ode</a> <a href="/tags/differential-equations"> differential-equations</a> <a href="/tags/epidemiology"> epidemiology</a> <a class="addNewTagLink" style="display:none">+ Manage Tags</a> </div> </div> </div> </div> <div class="clearfix"> </div> <div class="row text-center top2footerBG top2footer"><a href='/posts/225528-Exploring-The-SIR-Model-With-Vaccination'>Read Full Post</a></div> </div> </div> <!-- Top 2 posts end --> <br /> <!-- more posts --> <div id="morePosts"> <div class="listDoc" id='225303'> <div id="ctl00_MainContent__home_morePosts_ctrl0_PostHeader_header" class="post"> <div class="call"> <div class="post"> <div class="wrap-ut pull-left"> <div class="userinfo pull-left"> <div id="ctl00_MainContent__home_morePosts_ctrl0_PostHeader_photo_photoPanel" class="photo"> <a id="ctl00_MainContent__home_morePosts_ctrl0_PostHeader_photo_photoLink" href="/users/Paras31"> <div class="avatar"> <img src="https://www.maplesoft.com/content/MemberPhotos/\4065368_Paras31_20240422174152.jpeg" id="ctl00_MainContent__home_morePosts_ctrl0_PostHeader_photo_memberPhoto" width="75" height="75" /> </div> </a> <div id="editImage" style="background:rgba(0, 0, 0, .6) 70%; 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Please try again.</p> </div> </div> <div id="middle"> <table> <tr> <td> <label> E-Mail Address:</label> </td> <td> <input style="width: 200px; color: Black; margin-left: 3px;" type="text" id="userPanelEmail" name="userPanelEmail" /> </td> </tr> <tr> <td> <label style="padding-right: 40px;" for="userPass"> Password:</label> </td> <td> <input style="width: 200px; color: Black; margin-left: 3px;" type="password" id="userPanelPass" name="userPanelPass" autocomplete="false" /> </td> </tr> <tr> <td> <label> Remember Me:</label> </td> <td> <input type="checkbox" name="persistLogin" id="persistPanelLogin" checked="checked" />Automatically sign in on future visits </td> </tr> </table> <br /> </div> <div id="bottom"> <br /> <a href="http://www.maplesoft.com/members/member_center_passwordreset.aspx" target="_blank" style="float: right;">Forgot your password?</a> <a href="/register" target="_blank" style="float: left;">Create a New Account</a> </div> </div> </div> <div id="ctl00_sidebar" class="col-lg-3 col-md-3"> <!-- Sidebar Content Before Buttons--> <div class="hidden-sm hidden-xs" style="padding-bottom:20px;"> <!-- ask question --> <a href="/questions/new" style="color:#FFFFFF"><div class="sidebarblockquestion"> <h3><i class="fa fa-question-circle"></i> Ask a Question</h3> </div></a> <!-- create a post --> <a href="/posts/new" id="ctl00_aNewCategoryPost" style="color:#FFFFFF"><div class="sidebarblockcreatepost"> <h3><i class="fa fa-pencil"></i> Create a Post</h3> </div></a> </div> <!-- Sidebar Content After Buttons--> <div id="sidebarHolder"> </div> </div> </div> </div> </div> </section> <!-- footer nav --> <div class="shadow v4"> </div> <div id="footer"> <div class="container" style="padding-top: 30px;"> <div class="col-md-12" style="padding-bottom:10px;"> <div class="row" style="border-bottom: 1px solid #ececec;"> <div class="blocktxt center-block" style="padding-bottom:10px;"> <span style="font-size:16px; color:#ffffff;">Connect with Maplesoft:</span> <a href="http://www.facebook.com/Maplesoft" target="_blank"><i class="fa fa-facebook-square" style="font-size: 30px; padding-right:5px; color:#ffffff"></i></a> <a href="http://www.twitter.com/maplesoft" target="_blank"><i class="fa fa-twitter-square" style="font-size: 30px; padding-right:5px; color:#ffffff"> </i></a> <a href="http://www.linkedin.com/groups?home=&gid=1782256" target="_blank"><i class="fa fa-linkedin-square" style="font-size: 30px; padding-right:5px; color:#ffffff"> </i></a> <a href="http://www.youtube.com/MaplesoftVideo" target="_blank"><i class="fa fa-youtube-square" style="font-size: 30px; padding-right:5px; color:#ffffff"></i></a> </div> </div> </div> <div class="col-md-8"> <div class="row"> <a href="/questions">Questions</a> | <a href="/posts">Posts</a> | <a href="/tags">Tags</a> | <a href="/users">Users</a> | <a href="/unanswered">Unanswered</a> | <a href="/maplesoftblog">Maplesoft Blog</a> | <a href="/badges">Badges</a> | <a href="/recent"> Recent</a> </div> </div> <div class="col-md-4"> <div class="row"> <a href="/help/about">About</a> | <a href="/help">MaplePrimes Help</a> | <a href="https://faq.maplesoft.com/s/article/Maple-Primes-Support">Support</a><br> </div> </div> <div class="col-md-12"> <div class="row"> <div class="blocktxt" style="font-size: smaller;"> © Maplesoft, a division of Waterloo Maple Inc. <script type="text/javascript"> document.write(dateObject.getFullYear()); </script> . | <a href="http://www.maplesoft.com">maplesoft.com</a> | <a href="http://www.maplesoft.com/terms/">Terms of Use</a> | <a href="http://www.maplesoft.com/privacy/"> Privacy</a> | <a href="#" class="termly-display-preferences">Consent Preferences</a> | <a href="http://www.maplesoft.com/trademark/">Trademarks</a></p> <br> </div> </div> </div> </div> </div> <!-- end footer nav --> </div> <script src="/js/BadgeNotify.js" type="text/javascript"></script> <!-- PDF Generate Dialog Box Starts--> <div id="GeneratePDF" title="Save Page as PDF" style="display: none;"> <div id="top"> <div id="generatingPDF"> <h3 style="text-align: center;"> Generating PDF…</h3> <img alt="loading" style="display: block; margin-left: auto; margin-right: auto" src="/images/ajax-loader.gif" /> </div> <div id="downloadPDF" style="display: none; text-align: center;"> <span style="display: block; margin-left: auto; margin-right: auto" class='fa fa-file-pdf-o fa-2x'> <a href="" target="_blank" id="PDFLink">PDF ready for download.</a></span> </div> <div id="pdfGenerateError" style="display: none"> <p style="color: Red; text-align: center;"> Error occurred during PDF generation. Please refresh the page and try again</p> </div> </div> </div> <!-- PDF Generate Dialog Box Ends--> <!-- New Login Dialog box starts --> <!-- Modal --> <div id="loginModel" class="modal fade" role="dialog"> <div class="modal-dialog "> <!-- Modal content--> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal">×</button> <h4 class="modal-title text-center">Login to Your MaplePrimes Account</h4> </div> <div class="modal-body"> <div class="form-horizontal"> <div id="userModelLoginError" class="row" style="display:none;"> <div class="col-md-offset-2 col-md-10"> <p class="text-danger">Wrong Email/Password. Please try again.</p> </div> </div> <div class="row form-group"> <div class="col-md-4">E-Mail Address:</div> <div class="col-md-6"> <input type="email" class="form-control" required id="userModelEmail" name="userEmail" onkeydown = "if (event.keyCode == 13) document.getElementById('btnLogin').click()"/> </div> <div class="col-md-2"></div> </div> <div class="row form-group"> <div class="col-md-4">Password:</div> <div class="col-md-6"> <input class="form-control" type="password" required id="userModelPass" name="userPass" onkeydown = "if (event.keyCode == 13) document.getElementById('btnLogin').click()" autocomplete="false" /> </div> <div class="col-md-2"></div> </div> <div class="row form-group"> <div class="col-md-4">Remember Me:</div> <div class="col-md-6"> <input type="checkbox" name="persistLogin" id="userPersistLogin" checked="checked" />Automatically sign in on future visits </div> <div class="col-md-2"></div> </div> <div class="row form-group"> <div class="col-md-2"></div> <div class="col-md-4"><a href="http://www.maplesoft.com/members/member_center_passwordreset.aspx" target="_blank" class="btn-link btn-primary">Forgot your password?</a></div> <div class="col-md-4"> <a href="/register" target="_blank" class="btn-link btn-primary">Create a New Account</a> </div> <div class="col-md-2"></div> </div> </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-default btn-sm" data-dismiss="modal">Close</button> <button type="button" class="btn btn-primary btn-sm" onclick="memberlogin()" id="btnLogin">Login</button> </div> </div> </div> </div> <!-- New Login dialog box ends --> <!-- Focus email field when login modal is shown --> <script> $('#loginModel').on('shown.bs.modal', function() { $('#userModelEmail').focus(); }) </script> <script src="/ckeditor/ckeditor.js" type="text/javascript"></script> <script src="/ckeditor/adapters/jquery.js" type="text/javascript"></script> <script src="/js/newEditor.js?v=1" type="text/javascript"></script> </body> </html>
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