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<html>
<head>
<link rel="stylesheet" type="text/css" href="../distrib/jsxgraph.css" />
<script type="text/javascript" src="/javascript/prototype/prototype.js"></script>
<script type="text/javascript" src="../distrib/jsxgraphcore.js"></script>
</head>
<body>
<h1>Epidemien - SIR model without vital dynamics</h1>
<span style="color:Blue">Blue: Susceptible population rate</span><br>
<span style="color:red">Red: Infected population rate</span><br>
<span style="color:green">Green: Recovered population rate (which means: immune, isolated or dead)</span><br>
<form><input type="button" value="clear and run" onClick="clearturtle();run()"></form>
<div id="jsxgbox" class="jxgbox" style="width:600px; height:600px;"></div>
<script type="text/javascript">
var brd = JXG.JSXGraph.initBoard('jsxgbox', {originX: 20, originY: 300, unitX: 20, unitY: 250});
var S = brd.createElement('turtle',[],{strokeColor:'blue',strokeWidth:3});
var I = brd.createElement('turtle',[],{strokeColor:'red',strokeWidth:3});
var R = brd.createElement('turtle',[],{strokeColor:'green',strokeWidth:3});
var xaxis = brd.createElement('axis', [[0,0], [1,0]], {});
var yaxis = brd.createElement('axis', [[0,0], [0,1]], {});
var s = brd.createElement('slider', [[0,-0.5], [10,-0.5],[0,0.03,1]], {name:'s'});
brd.createElement('text', [12,-0.5, "initially infected population rate"]);
var beta = brd.createElement('slider', [[0,-0.6], [10,-0.6],[0,0.5,1]], {name:'β'});
brd.createElement('text', [12,-0.6, "β: infection rate"]);
var gamma = brd.createElement('slider', [[0,-0.7], [10,-0.7],[0,0.3,1]], {name:'γ'});
brd.createElement('text', [12,-0.7, "γ: recovery rate"]);
brd.createElement('text', [12,-0.4, function() {return "I(t)="+Math.round(I.pos[1],3);}]);
S.hideTurtle();
I.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() {
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]) {
setTimeout(loop,10);
}
}
//*/
</script>
<p>
Hong Kong flu: initially 7.9 million people, 10 infected, 0 recovered. Thus S(0) = 1, I(0) = 1.27E-6, R(0) = 0, see http://www.cs.princeton.edu/introcs/94diffeq/.
</body>
</html>
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