SIR model: swine flu: Difference between revisions

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* In [http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=2715422 Modeling influenza epidemics and pandemics: insights into the future of swine flu (H1N1)] the authors estimate the reproduction rate <math>R_0</math> of the virus to be about <math>2</math>. For the SIR model this means: the reproduction rate <math>R_0</math> for influenza is equal to the infection rate of the strain (<math>\beta</math>) multiplied by the duration of the infectious period (<math>1/\gamma</math>), i.e.  
* In [http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=2715422 Modeling influenza epidemics and pandemics: insights into the future of swine flu (H1N1)] the authors estimate the reproduction rate <math>R_0</math> of the virus to be about <math>2</math>. For the SIR model this means: the reproduction rate <math>R_0</math> for influenza is equal to the infection rate of the strain (<math>\beta</math>) multiplied by the duration of the infectious period (<math>1/\gamma</math>), i.e.  
:<math>\beta = R_0\cdot \gamma</math>. Therefore, we set the :<math>\beta = 2\cdot 1/7 = 0.2857</math>
:<math>\beta = R_0\cdot \gamma</math>. Therefore, we set the :<math>\beta = 2\cdot 1/7 = 0.2857</math>
* We run the simulation for a population of 1 million people, where 1 person is infected initially, i.e. <math>s= 1E-6</math>.
* We run the simulation for a population of 1 million people, where 1 person is infected initially, i.e. <math>s=1E{-6}</math>.
Thus S(0) = 1, I(0) = 1.E-6, R(0) = 0
Thus S(0) = 1, I(0) = 1.E-6, R(0) = 0
<html>
<html>
<form><input type="button" value="clear and run a simulation of 100 days" onClick="clearturtle();run()">
<form><input type="button" value="clear and run a simulation of 200 days" onClick="clearturtle();run()">
<input type="button" value="stop" onClick="stop()">
<input type="button" value="stop" onClick="stop()">
<input type="button" value="continue" onClick="goOn()"></form>
<input type="button" value="continue" onClick="goOn()"></form>
</html>
</html>
<jsxgraph width="700" height="500">
<jsxgraph width="700" height="500">
var brd = JXG.JSXGraph.initBoard('jxgbox', {originX: 20, originY: 300, unitX: 7, unitY: 250});
var brd = JXG.JSXGraph.initBoard('jxgbox', {originX: 20, originY: 300, unitX: 3, unitY: 250, axis:true});
   
   
var S = brd.createElement('turtle',[],{strokeColor:'blue',strokeWidth:3});
var S = brd.createElement('turtle',[],{strokeColor:'blue',strokeWidth:3});
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var R = brd.createElement('turtle',[],{strokeColor:'green',strokeWidth:3});
var R = brd.createElement('turtle',[],{strokeColor:'green',strokeWidth:3});
   
   
var xaxis = brd.createElement('axis', [[0,0], [1,0]], {});
var s = brd.createElement('slider', [[0,-0.3], [60,-0.3],[0,1E-6,1]], {name:'s'});
var yaxis = brd.createElement('axis', [[0,0], [0,1]], {});
var s = brd.createElement('slider', [[0,-0.3], [30,-0.3],[0,1E-6,1]], {name:'s'});
brd.createElement('text', [40,-0.3, "initially infected population rate"]);
brd.createElement('text', [40,-0.3, "initially infected population rate"]);
var beta = brd.createElement('slider', [[0,-0.4], [30,-0.4],[0,0.2857,1]], {name:'&beta;'});
var beta = brd.createElement('slider', [[0,-0.4], [60,-0.4],[0,0.2857,1]], {name:'&beta;'});
brd.createElement('text', [40,-0.4, "&beta;: infection rate"]);
brd.createElement('text', [40,-0.4, "&beta;: infection rate"]);
var gamma = brd.createElement('slider', [[0,-0.5], [30,-0.5],[0,0.1428,1]], {name:'&gamma;'});
var gamma = brd.createElement('slider', [[0,-0.5], [60,-0.5],[0,0.1428,1]], {name:'&gamma;'});
brd.createElement('text', [40,-0.5, "&gamma;: recovery rate = 1/(days of infection)"]);
brd.createElement('text', [40,-0.5, "&gamma;: recovery rate = 1/(days of infection)"]);
   
   
var t = 0; // global
var t = 0; // global
   
   
brd.createElement('text', [40,-0.2,  
brd.createElement('text', [90,-0.2,  
         function() {return "Day "+t+": infected="+brd.round(1000000*I.Y(),1)+" recovered="+brd.round(1000000*R.Y(),1);}]);
         function() {return "Day "+t+": infected="+brd.round(1000000*I.Y(),1)+" recovered="+brd.round(1000000*R.Y(),1);}]);
   
   
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   t += delta;
   t += delta;
   if (t<100.0) {
   if (t<200.0) {
     active = setTimeout(loop,10);
     active = setTimeout(loop,10);
   }
   }

Revision as of 11:31, 10 August 2009

The SIR model tries to model influenza epidemics. Here, we try to medel the spreading of the swine flu.

  • According to the CDC Centers of Disease Control and Prevention: "Adults shed influenza virus from the day before symptoms begin through 5-10 days after illness onset. However, the amount of virus shed, and presumably infectivity, decreases rapidly by 3-5 days after onset in an experimental human infection model." So, here we set [math]\displaystyle{ \gamma=1/7=0.1428 }[/math] as the recovery rate. This means, on average an infected person sheds the virus for 7 days.
  • In Modeling influenza epidemics and pandemics: insights into the future of swine flu (H1N1) the authors estimate the reproduction rate [math]\displaystyle{ R_0 }[/math] of the virus to be about [math]\displaystyle{ 2 }[/math]. For the SIR model this means: the reproduction rate [math]\displaystyle{ R_0 }[/math] for influenza is equal to the infection rate of the strain ([math]\displaystyle{ \beta }[/math]) multiplied by the duration of the infectious period ([math]\displaystyle{ 1/\gamma }[/math]), i.e.
[math]\displaystyle{ \beta = R_0\cdot \gamma }[/math]. Therefore, we set the :[math]\displaystyle{ \beta = 2\cdot 1/7 = 0.2857 }[/math]
  • We run the simulation for a population of 1 million people, where 1 person is infected initially, i.e. [math]\displaystyle{ s=1E{-6} }[/math].

Thus S(0) = 1, I(0) = 1.E-6, R(0) = 0

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