Difference between revisions of "SIR model: swine flu"

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The SIR model tries to model influenza epidemics. Here, we try to medel the spreading of the swine flu.
 
The SIR model tries to model influenza epidemics. Here, we try to medel the spreading of the swine flu.
* According to the [http://www.cdc.gov/ 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>\gamma=1/7</math> as the recovery rate. This means, on average an infected person sheds the virus for 7 days.
+
* According to the [http://www.cdc.gov/ 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>\gamma=1/7=0.1428</math> as the recovery rate. This means, on average an infected person sheds the virus for 7 days.
* 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 2. For the SIR model this means:
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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.  
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>
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* We run the simulation for a population of 1 million people, where 1 person is infected initially, i.e. <math>s= 1E-6</math>.
 
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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 100 days" onClick="clearturtle();run()">
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var yaxis = brd.createElement('axis', [[0,0], [0,1]], {});
 
var yaxis = brd.createElement('axis', [[0,0], [0,1]], {});
 
   
 
   
var s = brd.createElement('slider', [[0,-0.3], [30,-0.3],[0,0.03,1]], {name:'s'});
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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],[0,0.5,1]], {name:'&beta;'});
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var beta = brd.createElement('slider', [[0,-0.4], [30,-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],[0,0.166,1]], {name:'&gamma;'});
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var gamma = brd.createElement('slider', [[0,-0.5], [30,-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)"]);
 
   
 
   
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brd.createElement('text', [40,-0.2,  
 
brd.createElement('text', [40,-0.2,  
         function() {return "Day "+t+": infected="+brd.round(7900000*I.Y(),1)+" recovered="+brd.round(7900000*R.Y(),1);}]);
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         function() {return "Day "+t+": infected="+brd.round(1000000*I.Y(),1)+" recovered="+brd.round(1000000*R.Y(),1);}]);
 
   
 
   
 
S.hideTurtle();
 
S.hideTurtle();

Revision as of 12:29, 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]\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]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]
  • 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