Epidemiology: The SIR model: Difference between revisions
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I.hideTurtle(); | I.hideTurtle(); | ||
R.hideTurtle(); | R.hideTurtle(); | ||
function clearturtle() { | |||
S.cs(); | |||
I.cs(); | |||
R.cs(); | |||
S.hideTurtle(); | |||
I.hideTurtle(); | |||
R.hideTurtle(); | |||
} | |||
function run() { | |||
S.setPos(0,1.0-s.Value()); | |||
R.setPos(0,0); | |||
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)
