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" 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"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEnJiM5NjE7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGNC8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictRi82I1EhRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi5RIn5GJ0Y1RjcvJSZmZW5jZUdGNC8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZURjVGNw==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEnJiM5NjE7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGNC8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictRi82I1EhRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi5RIn5GJ0Y1RjcvJSZmZW5jZUdGNC8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZURjVGNw==</Equation><Font subscript="true" family="Arial" italic="true"> </Font><Font family="Arial">is the number of secondary infections that is produced by one primary infection in a wholly susceptible population. Only when </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEnJiM5NjE7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGNC8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictRi82I1EhRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi5RIn5GJ0Y1RjcvJSZmZW5jZUdGNC8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZURjVGNw==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEnJiM5NjE7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGNC8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictRi82I1EhRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi5RIn5GJ0Y1RjcvJSZmZW5jZUdGNC8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZURjVGNw==</Equation><Font family="Arial" italic="true"> &gt; </Font><Font family="Arial">1<Font italic="true">, </Font>does<Font italic="true"> </Font>an epidemic occurs. <Font encoding="UTF-8">1/(\316\263+\316\274)</Font> is the average infectious period. Setting equations (1)-(3) equal to zero and solving these for the equilibrium solutions of </Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font family="Arial"> and </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JlEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNiUtRiw2JlEidEYnRi9GMkY1RjIvRjZRJ25vcm1hbEYnRjJGQC1GLDYjUSFGJ0YyRkA=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JlEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNiUtRiw2JlEidEYnRi9GMkY1RjIvRjZRJ25vcm1hbEYnRjJGQC1GLDYjUSFGJ0YyRkA=</Equation><Font family="Arial"> in dependence of the parameters </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2JlEnJiM5NTY7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGMS8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYuUSIsRidGMkY0LyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHUSV0cnVlRicvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRjg2LlEifkYnRjJGNEY7L0Y+RjFGQEZCRkRGRkZIRkovRk5GTC1GLDYmUScmIzk0NjtGJ0YvRjJGNEY3RjJGNA==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2JlEnJiM5NTY7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGMS8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYuUSIsRidGMkY0LyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHUSV0cnVlRicvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRjg2LlEifkYnRjJGNEY7L0Y+RjFGQEZCRkRGRkZIRkovRk5GTC1GLDYmUScmIzk0NjtGJ0YvRjJGNEY3RjJGNA==</Equation><Font family="Arial">and </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JlEnJiM5NDc7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGMS8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYuUSJ+RidGMkY0LyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGS0Y3RjJGNA==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JlEnJiM5NDc7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGMS8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYuUSJ+RidGMkY0LyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGS0Y3RjJGNA==</Equation><Font family="Arial">(e.g. by using the Maple procedure <Font italic="true">solve()</Font>) provides the following equilibrium solution:</Font></Text-field>
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<Input><Text-field style="Text" layout="Normal"><Font bold="true" family="Arial">Notes</Font><Font family="Arial">: (1) The basic reproduction ratio </Font><Equation executable="true" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEnJiM5NjE7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GLzYjUSFGJy8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnLUkjbW9HRiQ2LVEifkYnRjUvJSZmZW5jZUdGNC8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZSLyUrZXhlY3V0YWJsZUdGNEY1">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEnJiM5NjE7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GLzYjUSFGJy8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnLUkjbW9HRiQ2LVEifkYnRjUvJSZmZW5jZUdGNC8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZSLyUrZXhlY3V0YWJsZUdGNEY1</Equation><Font family="Arial">is often ambiguously denoted </Font><Equation executable="true" style="2D Math" input-equation="" display="LUklbXN1Ykc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYsNiZRIjBGJ0YvRjJGNS8lL3N1YnNjcmlwdHNoaWZ0R0Y6">LUklbXN1Ykc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYsNiZRIjBGJ0YvRjJGNS8lL3N1YnNjcmlwdHNoaWZ0R0Y6</Equation><Font family="Arial">, leading to potential confusion with </Font><Equation executable="true" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNiQtSSNtbkdGJDYlUSIwRidGMi9GNlEnbm9ybWFsRidGQUYyRkFGQQ==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNiQtSSNtbkdGJDYlUSIwRidGMi9GNlEnbm9ybWFsRidGQUYyRkFGQQ==</Equation><Font family="Arial">, which is the initial value of the recovered function </Font><Equation executable="true" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNiQtRiw2JlEidEYnRi9GMkY1L0Y2USdub3JtYWxGJ0YyRkBGQA==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNiQtRiw2JlEidEYnRi9GMkY1L0Y2USdub3JtYWxGJ0YyRkBGQA==</Equation><Font family="Arial">. (2) Not all combinations of infection and removal rates within the ranges of the interactive model below will match a real existing infectious disease. (3)The SIR model exists in different flavors and parametrizations, the model as presented here follows Bloomfield[2009].</Font></Text-field>
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