Difference between revisions of "Epidemiology: The SIR model"

From JSXGraph Wiki
Jump to navigationJump to search
Line 21: Line 21:
 
<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" onClick="clearturtle();run()"></form>
 
<form><input type="button" value="clear and run" onClick="clearturtle();run()"></form>
<div id="box" class="jxgbox" style="width:450px; height:600px;"></div>
+
<div id="box" class="jxgbox" style="width:600px; height:450px;"></div>
 
<script language="JavaScript">
 
<script language="JavaScript">
 
var brd = JXG.JSXGraph.initBoard('box', {originX: 20, originY: 300, unitX: 20, unitY: 250});
 
var brd = JXG.JSXGraph.initBoard('box', {originX: 20, originY: 300, unitX: 20, unitY: 250});

Revision as of 19:46, 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] \frac{dS}{dt} = - \beta I S [/math]
[math] \frac{dR}{dt} = \gamma I [/math]
[math] \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)