Epidemiology: The SIR model: Difference between revisions

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Simulation of differential equations with turtle graphics using [[http://jsxgraph.org JSXGraph]].
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===SIR model without vital dynamics===
===SIR model without vital dynamics===
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:<math> \frac{dI}{dt} = -(dS+dR) </math>
:<math> \frac{dI}{dt} = -(dS+dR) </math>
The lines in the JSXGraph-simulation below have the following meaning:
* <span style="color:Blue">Blue: Rate of susceptible population</span>
* <span style="color:red">Red: Rate of infected population</span>
* <span style="color:green">Green: Rate of recovered population (which means: immune, isolated or dead)




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Revision as of 17:37, 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)