Epidemiology: The SIR model - Revision history

A WASSERMANN at 14:59, 20 February 2013

2013-02-20T14:59:26Z

← Older revision		Revision as of 14:59, 20 February 2013
Line 50:		Line 50:

	brd.create('text', [40,-0.2,		brd.create('text', [40,-0.2,
	function() {return "Day "+t+": infected="+~~brd.round~~(7900000I.Y(),1)+" recovered="+~~brd.round~~(7900000R.Y(),1);}]);		function() {return "Day "+t+": infected="+(7900000I.Y()).toFixed(1)+" recovered="+(7900000R.Y()).toFixed(1);}]);

	S.hideTurtle();		S.hideTurtle();
Line 128:		Line 128:

	brd.create('text', [40,-0.2,		brd.create('text', [40,-0.2,
	function() {return "Day "+t+": infected="+~~brd.round~~(7900000I.Y(),1)+" recovered="+~~brd.round~~(7900000R.Y(),1);}]);		function() {return "Day "+t+": infected="+(7900000I.Y()).toFixed(1)+" recovered="+(7900000R.Y()).toFixed(1);}]);

	S.hideTurtle();		S.hideTurtle();

Michael at 13:54, 7 June 2011

2011-06-07T13:54:55Z

← Older revision		Revision as of 13:54, 7 June 2011
Line 28:		Line 28:
	* <span style="color:green">Green: Rate of recovered population (which means: immune, isolated or dead)		* <span style="color:green">Green: Rate of recovered population (which means: immune, isolated or dead)
	<html>		<html>
	~~<link rel="stylesheet" type="text/css" href="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraph.css" />~~
	~~<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraphcore.js"></script>~~
	<form><input type="button" value="clear and run a simulation of 100 days" onClick="clearturtle();run()">		<form><input type="button" value="clear and run a simulation of 100 days" onClick="clearturtle();run()">
	<input type="button" value="stop" onClick="stop()">		<input type="button" value="stop" onClick="stop()">
	<input type="button" value="continue" onClick="goOn()"></form>		<input type="button" value="continue" onClick="goOn()"></form>
	~~<div id="box" class="jxgbox" style="width:600px; height:450px;">~~</~~div>~~		</html>
	~~<script language="JavaScript"~~>
	~~var brd = JXG.JSXGraph.initBoard('box', {originX: 20, originY: 300, unitX: 6, unitY: 250});~~

	var S = brd.~~createElement~~('turtle',[],{strokeColor:'blue',strokeWidth:3});		<jsxgraph box="box" width="600" height="450">
	var I = brd.~~createElement~~('turtle',[],{strokeColor:'red',strokeWidth:3});		var brd = JXG.JSXGraph.initBoard('box', {axis: true, boundingbox: [-5, 1.2, 100, -1.2]});
	var R = brd.~~createElement~~('turtle',[],{strokeColor:'green',strokeWidth:3});
			var S = brd.create('turtle',[],{strokeColor:'blue',strokeWidth:3});
			var I = brd.create('turtle',[],{strokeColor:'red',strokeWidth:3});
			var R = brd.create('turtle',[],{strokeColor:'green',strokeWidth:3});

	~~var xaxis = brd.createElement('axis', [[0,0], [1,0]], {});~~		var s = brd.create('slider', [[0,-0.3], [30,-0.3],[0,1.27E-6,1]], {name:'s'});
	~~var yaxis = brd.createElement('axis', [[0,0], [0,1]], {});~~		brd.create('text', [40,-0.3, "initially infected population rate (on load: I(0)=1.27E-6)"]);
			var beta = brd.create('slider', [[0,-0.4], [30,-0.4],[0,0.5,1]], {name:'β'});
	var s = brd.~~createElement~~('slider', [[0,-0.3], [30,-0.3],[0,1.27E-6,1]], {name:'s'});		brd.create('text', [40,-0.4, "β: infection rate"]);
	brd.~~createElement~~('text', [40,-0.3, "initially infected population rate (on load: I(0)=1.27E-6)"]);		var gamma = brd.create('slider', [[0,-0.5], [30,-0.5],[0,0.3,1]], {name:'γ'});
	var beta = brd.~~createElement~~('slider', [[0,-0.4], [30,-0.4],[0,0.5,1]], {name:'β'});		brd.create('text', [40,-0.5, "γ: recovery rate = 1/(days of infection)"]);
	brd.~~createElement~~('text', [40,-0.4, "β: infection rate"]);
	var gamma = brd.~~createElement~~('slider', [[0,-0.5], [30,-0.5],[0,0.3,1]], {name:'γ'});
	brd.~~createElement~~('text', [40,-0.5, "γ: recovery rate = 1/(days of infection)"]);

	var t = 0; // global		var t = 0; // global

	brd.~~createElement~~('text', [40,-0.2,		brd.create('text', [40,-0.2,
	function() {return "Day "+t+": infected="+brd.round(7900000I.Y(),1)+" recovered="+brd.round(7900000R.Y(),1);}]);		function() {return "Day "+t+": infected="+brd.round(7900000I.Y(),1)+" recovered="+brd.round(7900000R.Y(),1);}]);

Line 112:		Line 108:

	}		}
	</~~script>~~		</jsxgraph>
	~~</html~~>

	===The underlying JavaScript code===		===The underlying JavaScript code===
	~~<source lang="html4strict">~~
	~~<link rel="stylesheet" type="text/css" href="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraph.css" />~~
	~~<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraphcore.js"></script>~~
	~~<form><input type="button" value="clear and run a simulation of 100 days" onClick="clearturtle();run()">~~
	~~<input type="button" value="stop" onClick="stop()">~~
	~~<input type="button" value="continue" onClick="goOn()"></form>~~
	~~<div id="box" class="jxgbox" style="width:600px; height:450px;"></div>~~
	~~</source>~~

	<source lang="javascript">		<source lang="javascript">
	var brd = JXG.JSXGraph.initBoard('box', {~~originX~~: 20, ~~originY~~: ~~300~~, ~~unitX: 20~~, ~~unitY: 250~~});		var brd = JXG.JSXGraph.initBoard('box', {axis: true, boundingbox: [-5, 1.2, 100, -1.2]});

	var S = brd.~~createElement~~('turtle',[],{strokeColor:'blue',strokeWidth:3});		var S = brd.create('turtle',[],{strokeColor:'blue',strokeWidth:3});
	var I = brd.~~createElement~~('turtle',[],{strokeColor:'red',strokeWidth:3});		var I = brd.create('turtle',[],{strokeColor:'red',strokeWidth:3});
	var R = brd.~~createElement~~('turtle',[],{strokeColor:'green',strokeWidth:3});		var R = brd.create('turtle',[],{strokeColor:'green',strokeWidth:3});

	~~var xaxis = brd.createElement('axis', [[0,0], [1,0]], {});~~		var s = brd.create('slider', [[0,-0.3], [30,-0.3],[0,1.27E-6,1]], {name:'s'});
	~~var yaxis = brd.createElement('axis', [[0,0], [0,1]], {});~~		brd.create('text', [40,-0.3, "initially infected population rate (on load: I(0)=1.27E-6)"]);
			var beta = brd.create('slider', [[0,-0.4], [30,-0.4],[0,0.5,1]], {name:'β'});
	var s = brd.~~createElement~~('slider', [[0,-0.3], [30,-0.3],[0,0.03,1]], {name:'s'});		brd.create('text', [40,-0.4, "β: infection rate"]);
	brd.~~createElement~~('text', [40,-0.3, "initially infected population rate"]);		var gamma = brd.create('slider', [[0,-0.5], [30,-0.5],[0,0.3,1]], {name:'γ'});
	var beta = brd.~~createElement~~('slider', [[0,-0.4], [30,-0.4],[0,0.5,1]], {name:'β'});		brd.create('text', [40,-0.5, "γ: recovery rate = 1/(days of infection)"]);
	brd.~~createElement~~('text', [40,-0.4, "β: infection rate"]);
	var gamma = brd.~~createElement~~('slider', [[0,-0.5], [30,-0.5],[0,0.3,1]], {name:'γ'});
	brd.~~createElement~~('text', [40,-0.5, "γ: recovery rate = 1/(days of infection)"]);

	var t = 0; // global		var t = 0; // global

	brd.~~createElement~~('text', [40,-0.2,		brd.create('text', [40,-0.2,
	function() {return "Day "+t+": infected="+brd.round(7900000I.Y(),1)+" recovered="+brd.round(7900000R.Y(),1);}]);		function() {return "Day "+t+": infected="+brd.round(7900000I.Y(),1)+" recovered="+brd.round(7900000R.Y(),1);}]);

Line 188:		Line 171:
	}		}
	}		}

	function stop() {		function stop() {
	if (active) clearTimeout(active);		if (active) clearTimeout(active);

A WASSERMANN at 06:57, 4 June 2010

2010-06-04T06:57:06Z

← Older revision		Revision as of 06:57, 4 June 2010
Line 206:		Line 206:
	===See also===		===See also===
	* [[Epidemiology: The SEIR model]]		* [[Epidemiology: The SEIR model]]
			* [[Population growth models]]
			* [[Lotka-Volterra equations]]

	===References===		===References===

A WASSERMANN at 16:34, 29 October 2009

2009-10-29T16:34:36Z

← Older revision		Revision as of 16:34, 29 October 2009
Line 29:		Line 29:
	<html>		<html>
	<link rel="stylesheet" type="text/css" href="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraph.css" />		<link rel="stylesheet" type="text/css" href="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraph.css" />
	~~<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/prototype.js"></script>~~
	<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraphcore.js"></script>		<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraphcore.js"></script>
	<form><input type="button" value="clear and run a simulation of 100 days" onClick="clearturtle();run()">		<form><input type="button" value="clear and run a simulation of 100 days" onClick="clearturtle();run()">
Line 119:		Line 118:
	<source lang="html4strict">		<source lang="html4strict">
	<link rel="stylesheet" type="text/css" href="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraph.css" />		<link rel="stylesheet" type="text/css" href="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraph.css" />
	~~<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/prototype.js"></script>~~
	<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraphcore.js"></script>		<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraphcore.js"></script>
	<form><input type="button" value="clear and run a simulation of 100 days" onClick="clearturtle();run()">		<form><input type="button" value="clear and run a simulation of 100 days" onClick="clearturtle();run()">

A WASSERMANN at 07:54, 23 June 2009

2009-06-23T07:54:38Z

← Older revision		Revision as of 07:54, 23 June 2009
Line 55:		Line 55:

	brd.createElement('text', [40,-0.2,		brd.createElement('text', [40,-0.2,
	function() {return "Day "+t+": infected="+brd.round(7900000I.~~pos[1]~~,1)+" recovered="+brd.round(7900000R.~~pos[1]~~,1);}]);		function() {return "Day "+t+": infected="+brd.round(7900000I.Y(),1)+" recovered="+brd.round(7900000R.Y(),1);}]);

	S.hideTurtle();		S.hideTurtle();
Line 74:		Line 74:
	S.setPos(0,1.0-s.Value());		S.setPos(0,1.0-s.Value());
	R.setPos(0,0);		R.setPos(0,0);
	I.setPos(0,s.X());		I.setPos(0,s.Value());

	delta = 1; // global		delta = 1; // global
Line 82:		Line 82:

	function turtleMove(turtle,dx,dy) {		function turtleMove(turtle,dx,dy) {
	turtle.moveTo([dx+turtle.~~pos[0]~~,dy+turtle.~~pos[1]~~]);		turtle.moveTo([dx+turtle.X(),dy+turtle.Y()]);
	}		}

	function loop() {		function loop() {
	var dS = -beta.Value()S.~~pos[1]~~I.~~pos[1]~~;		var dS = -beta.Value()S.Y()I.Y();
	var dR = gamma.Value()*I.~~pos[1]~~;		var dR = gamma.Value()*I.Y();
	var dI = -(dS+dR);		var dI = -(dS+dR);
	turtleMove(S,delta,dS);		turtleMove(S,delta,dS);
Line 147:		Line 147:

	brd.createElement('text', [40,-0.2,		brd.createElement('text', [40,-0.2,
	function() {return "Day "+t+": infected="+brd.round(7900000I.~~pos[1]~~,1)+" recovered="+brd.round(7900000R.~~pos[1]~~,1);}]);		function() {return "Day "+t+": infected="+brd.round(7900000I.Y(),1)+" recovered="+brd.round(7900000R.Y(),1);}]);

	S.hideTurtle();		S.hideTurtle();
Line 166:		Line 166:
	S.setPos(0,1.0-s.Value());		S.setPos(0,1.0-s.Value());
	R.setPos(0,0);		R.setPos(0,0);
	I.setPos(0,s.X());		I.setPos(0,s.Value());

	delta = 1; // global		delta = 1; // global
Line 174:		Line 174:

	function turtleMove(turtle,dx,dy) {		function turtleMove(turtle,dx,dy) {
	turtle.moveTo([dx+turtle.~~pos[0]~~,dy+turtle.~~pos[1]~~]);		turtle.moveTo([dx+turtle.X(),dy+turtle.Y()]);
	}		}

	function loop() {		function loop() {
	var dS = -beta.Value()S.~~pos[1]~~I.~~pos[1]~~;		var dS = -beta.Value()S.Y()I.Y();
	var dR = gamma.Value()*I.~~pos[1]~~;		var dR = gamma.Value()*I.Y();
	var dI = -(dS+dR);		var dI = -(dS+dR);
	turtleMove(S,delta,dS);		turtleMove(S,delta,dS);
Line 187:		Line 187:
	t += delta;		t += delta;
	if (t<100.0) {		if (t<100.0) {
	setTimeout(loop,10);		active = setTimeout(loop,10);
	}		}
	}		}

A WASSERMANN at 08:08, 27 April 2009

2009-04-27T08:08:45Z

← Older revision		Revision as of 08:08, 27 April 2009
Line 205:		Line 205:
	}		}
	</source>		</source>

			===See also===
			* [[Epidemiology: The SEIR model]]

	===References===		===References===

A WASSERMANN at 07:49, 27 April 2009

2009-04-27T07:49:06Z

← Older revision		Revision as of 07:49, 27 April 2009
Line 83:		Line 83:
	function turtleMove(turtle,dx,dy) {		function turtleMove(turtle,dx,dy) {
	turtle.moveTo([dx+turtle.pos[0],dy+turtle.pos[1]]);		turtle.moveTo([dx+turtle.pos[0],dy+turtle.pos[1]]);
	~~//turtle.lookTo([1.0+turtle.pos[0],dy+turtle.pos[1]]);~~
	~~//turtle.fd(dxMath.sqrt(1+dydy));~~
	}		}

Line 176:		Line 174:

	function turtleMove(turtle,dx,dy) {		function turtleMove(turtle,dx,dy) {
	turtle.~~lookTo~~([~~1.0~~+turtle.pos[0],dy+turtle.pos[1]]);		turtle.moveTo([dx+turtle.pos[0],dy+turtle.pos[1]]);
	~~turtle.fd(dxMath.sqrt(1+dydy)~~);
	}		}

A WASSERMANN at 07:48, 27 April 2009

2009-04-27T07:48:07Z

← Older revision		Revision as of 07:48, 27 April 2009
Line 82:		Line 82:

	function turtleMove(turtle,dx,dy) {		function turtleMove(turtle,dx,dy) {
	turtle.lookTo([1.0+turtle.pos[0],dy+turtle.pos[1]]);		turtle.moveTo([dx+turtle.pos[0],dy+turtle.pos[1]]);
	turtle.fd(dxMath.sqrt(1+dydy));		//turtle.lookTo([1.0+turtle.pos[0],dy+turtle.pos[1]]);
			//turtle.fd(dxMath.sqrt(1+dydy));
	}		}

A WASSERMANN at 12:28, 22 January 2009

2009-01-22T12:28:51Z

← Older revision		Revision as of 12:28, 22 January 2009
Line 114:		Line 114:

	}		}


	</script>		</script>
	</html>		</html>
Line 124:		Line 122:
	<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/prototype.js"></script>		<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/prototype.js"></script>
	<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraphcore.js"></script>		<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraphcore.js"></script>
	<form><input type="button" value="clear and run a simulation of 100 days" onClick="clearturtle();run()"></form>		<form><input type="button" value="clear and run a simulation of 100 days" onClick="clearturtle();run()">
			<input type="button" value="stop" onClick="stop()">
			<input type="button" value="continue" onClick="goOn()"></form>
	<div id="box" class="jxgbox" style="width:600px; height:450px;"></div>		<div id="box" class="jxgbox" style="width:600px; height:450px;"></div>
	</source>		</source>
Line 191:		Line 191:
	setTimeout(loop,10);		setTimeout(loop,10);
	}		}
	}</source>		}
			function stop() {
			if (active) clearTimeout(active);
			active = null;
			}
			function goOn() {
			if (t>0) {
			if (active==null) {
			active = setTimeout(loop,10);
			}
			} else {
			run();
			}

			}
			</source>

	===References===		===References===

A WASSERMANN at 12:27, 22 January 2009

2009-01-22T12:27:23Z

← Older revision		Revision as of 12:27, 22 January 2009
Line 33:		Line 33:
	<form><input type="button" value="clear and run a simulation of 100 days" onClick="clearturtle();run()">		<form><input type="button" value="clear and run a simulation of 100 days" onClick="clearturtle();run()">
	<input type="button" value="stop" onClick="stop()">		<input type="button" value="stop" onClick="stop()">
	<input type="button" value="continue" onClick="~~continue~~()"></form>		<input type="button" value="continue" onClick="goOn()"></form>
	<div id="box" class="jxgbox" style="width:600px; height:450px;"></div>		<div id="box" class="jxgbox" style="width:600px; height:450px;"></div>
	<script language="JavaScript">		<script language="JavaScript">
Line 104:		Line 104:
	active = null;		active = null;
	}		}
	function ~~continue~~() {		function goOn() {
	if (t>0) {		if (t>0) {
	if (active==null) {		if (active==null) {