Epidemiology: The SIR model: Difference between revisions

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I.hideTurtle();
I.hideTurtle();
R.hideTurtle();
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function clearturtle() {
  S.cs();
  I.cs();
  R.cs();
  S.hideTurtle();
  I.hideTurtle();
  R.hideTurtle();
}
           
function run() {
  S.setPos(0,1.0-s.Value());
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  I.setPos(0,s.X());
               
  delta = 0.1; // global
  t = 0.0;  // global
  loop();
}
           
function turtleMove(turtle,dx,dy) {
  turtle.lookTo([1.0+turtle.pos[0],dy+turtle.pos[1]]);
  turtle.fd(dx*Math.sqrt(1+dy*dy));
}
           
function loop() {
}
              
              
</script>
</script>
</html>
</html>

Revision as of 17:41, 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)