Infectious-Disease-Modeling/NLCModel02.mw

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<Startup-Code startupcode="restart; \012interface(warnlevel = 0); \012with(DETools);\012with(plots); \012with(plottools); \012\012SIRclassic := module()\012\012local SIR, SU_0, In_0, R_0, N, SIRsol, m, b, g ;\012export MakePlotSIRsol ;\012uses DT=DocumentTools;\012\012#m: mu\012#b: beta\012#g: gamma\012\012\012SIR:=diff(Su(t),t)=m -b*Su(t)*In(t)-m*Su(t),diff(In(t),t)=b*Su(t)*In(t)-g*In(t)-m*In(t), diff(R(t),t)=g*In(t)-m*R(t);\012\012Su_0:=0.99; \012In_0:=0.01;\012R_0:=0; \012\012\012SIRsol:=dsolve({SIR, Su(0)=Su_0, In(0)=In_0, R(0) = R_0},{Su(t), In(t), R(t)}, parameters=[m, b ,g], type=numeric, output=listprocedure);\012\012MakePlotSIRsol:=proc()\012 uses plots, DocumentTools:\012 na:=&quot;not available&quot;; \012 DT:-Do(rez_mu = %Slider_rez_mu1);\012 DT:-Do(b = %Slider_beta1);\012 DT:-Do(g = %Slider_gamma1);\012 m:=1/rez_mu;\012 SIRsol(parameters=[ m, b, g]);\012 Susol:=subs(SIRsol, Su(t));\012 Insol:=subs(SIRsol, In(t));\012 Rsol :=subs(SIRsol, R(t));\012 Do(%Plot01=plot([Susol, Insol, Rsol],0..200.0, 0..1, color=[blue, red, cyan], font=[Helvetica, 10], labelfont=[Helvetica, 10], legend=[Susceptible, Infected , Recovered], labels=[&quot;Time&quot;,&quot;&quot;]));\012 Do(SetProperty(TextSu1,'value', sprintf(&quot;%10.5f&quot;, Su_0)));\012 Do(SetProperty(TextIn1,'value', sprintf(&quot;%10.5f&quot;, In_0)));\012 Do(SetProperty(TextR1,'value', sprintf(&quot;%10.5f&quot;, R_0)));\012 Do(SetProperty(Textmu1,'value', sprintf(&quot;%10.5f&quot;, m)));\012 Do(SetProperty(TextLE1,'value', sprintf(&quot;%10.5f&quot;, rez_mu)));\012 Do(SetProperty(Textbeta1,'value', sprintf(&quot;%10.5f&quot;,b)));\012 Do(SetProperty(Textgamma1,'value', sprintf(&quot;%10.5f&quot;,g)));\012 RNull:= b/(g+m) ;\012 Do(SetProperty(TextRNull1,'value', sprintf(&quot;%10.5f&quot;,RNull)));\012 if RNull &gt; 1 then;\012 Seq:=1/RNull;\012 Do(SetProperty(TextSeq1,'value', sprintf(&quot;%10.5f&quot;,Seq)));\012 Ieq:=(m/b)*(RNull-1);\012 Do(SetProperty(TextIeq1,'value', sprintf(&quot;%10.5f&quot;,Ieq)));\012 Req:=1-Seq-Ieq;\012 Do(SetProperty(TextReq1,'value', sprintf(&quot;%10.5f&quot;,Req)));\012 else;\012 \009 Do(SetProperty(TextSeq1, 'value', na));\012 \009 Do(SetProperty(TextIeq1, 'value', na));\012 \009 Do(SetProperty(TextReq1, 'value', na));\012 end if;\012 \012end proc;#MakePlotSIRsol\012\012end module;#SIRclassic\012\012# Initialize interactive document:\012DocumentTools:-SetProperty(Slider_rez_mu1, 'value', 80 );\012DocumentTools:-SetProperty(Slider_beta1, 'value', 0.25);\012DocumentTools:-SetProperty(Slider_gamma1, 'value', 0.1 );\012SIRclassic:-MakePlotSIRsol() ;"/>
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<Input><Text-field style="Text" family="Arial" layout="Normal"><Font family="Arial">The classical <Font bold="true">SIR</Font> model assumes that a population can be divided into three distinct compartments (see e.g. Bloomfield[2009, pp 149]): <Font bold="true">S</Font> is the proportion of susceptibles, <Font bold="true">I</Font> is the proportion of infected persons and <Font bold="true">R</Font><Font italic="true"> </Font>is the proportion of persons that have recovered from infection and are now immune against the disease. This model was originally developed in 1927 by Kermack and McKendrik. </Font></Text-field>
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<Input><Text-field style="Text" layout="Normal"><Font family="Arial">The <Font bold="true">basic reproduction ratio</Font> </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEnJiM5NjE7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGNC8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictRi82I1EhRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Y6RjVGNw==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEnJiM5NjE7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGNC8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictRi82I1EhRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Y6RjVGNw==</Equation><Font family="Arial">, for the SIR model as defined above, can be derived as: </Font></Text-field>
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<Input><Text-field style="Text" layout="Normal"><Font family="Arial">Kermack WO, McKendrick AG [1927]: <Font italic="true">A contribution to the Mathematical Theory of Epidemics.</Font> Proc. Roy. Soc. A 115, 700-711 </Font><Hyperlink linktarget="http://rspa.royalsocietypublishing.org/content/115/772/700" hyperlink="true"><Font underline="true" style="Text" foreground="[0,128,128]" family="Arial">(Download link)</Font></Hyperlink> </Text-field>
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