Epidemiology: The SIR model: Difference between revisions
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var yaxis = brd.createElement('axis', [[0,0], [0,1]], {}); | var yaxis = brd.createElement('axis', [[0,0], [0,1]], {}); | ||
var s = brd.createElement('slider', [[0,-0. | var s = brd.createElement('slider', [[0,-0.3], [10,-0.3],[0,0.03,1]], {name:'s'}); | ||
brd.createElement('text', [12,-0.5, "initially infected population rate"]); | brd.createElement('text', [12,-0.5, "initially infected population rate"]); | ||
var beta = brd.createElement('slider', [[0,-0. | var beta = brd.createElement('slider', [[0,-0.4], [10,-0.4],[0,0.5,1]], {name:'β'}); | ||
brd.createElement('text', [12,-0.6, "β: infection rate"]); | brd.createElement('text', [12,-0.6, "β: infection rate"]); | ||
var gamma = brd.createElement('slider', [[0,-0. | var gamma = brd.createElement('slider', [[0,-0.5], [10,-0.5],[0,0.3,1]], {name:'γ'}); | ||
brd.createElement('text', [12,-0.7, "γ: recovery rate"]); | brd.createElement('text', [12,-0.7, "γ: recovery rate"]); | ||
Revision as of 17:46, 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]\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)
