Epidemiology: The SIR model: Difference between revisions

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

Revision as of 17:42, 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]\displaystyle{ \frac{dS}{dt} = - \beta I S }[/math]
[math]\displaystyle{ \frac{dR}{dt} = \gamma I }[/math]
[math]\displaystyle{ \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)