Epidemiology: The SIR model: Difference between revisions
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I.cs(); | I.cs(); | ||
R.cs(); | R.cs(); | ||
/* | |||
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)
