Difference between revisions of "Epidemiology: The SIR model"

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   I.cs();
 
   I.cs();
 
   R.cs();
 
   R.cs();
  S.hideTurtle();
+
/* 
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S.hideTurtle();
 
   I.hideTurtle();
 
   I.hideTurtle();
 
   R.hideTurtle();
 
   R.hideTurtle();
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*/
 
}
 
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function loop() {
 
function loop() {
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  var dS = -beta.Value()*S.pos[1]*I.pos[1];
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  var dR = gamma.Value()*I.pos[1];
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  var dI = -(dS+dR);
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  turtleMove(S,delta,dS);
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  turtleMove(R,delta,dR);
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  turtleMove(I,delta,dI);
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  t += delta;
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  if (t<20.0 && I.pos[1]>0.00) {
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    setTimeout(loop,10);
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  }
 
}
 
}
 
              
 
              
 
</script>
 
</script>
 
</html>
 
</html>

Revision as of 18:42, 21 January 2009

Simulation of differential equations with turtle graphics using JSXGraph.

SIR model without vital dynamics

A single epidemic outbreak is usually far more rapid than the vital dynamics of a population, thus, if the aim is to study the immediate consequences of a single epidemic, one may neglect the birth-death processes. In this case the SIR system described above can be expressed by the following set of differential equations:

[math] \frac{dS}{dt} = - \beta I S [/math]
[math] \frac{dR}{dt} = \gamma I [/math]
[math] \frac{dI}{dt} = -(dS+dR) [/math]

The lines in the JSXGraph-simulation below have the following meaning:

* Blue: Rate of susceptible population
* Red: Rate of infected population
* Green: Rate of recovered population (which means: immune, isolated or dead)