Epidemiology: The SIR model: Difference between revisions

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The lines in the JSXGraph-simulation have the following meaning:
The lines in the JSXGraph-simulation have the following meaning:
  * <span style="color:Blue">Blue: Susceptible population rate</span><br>
  * <span style="color:Blue">Blue: Rate of susceptible population</span><br>
  * <span style="color:red">Red: Infected population rate</span><br>
  * <span style="color:red">Red: Rate of infected population</span><br>
  * <span style="color:green">Green: Recovered population rate (which means: immune, isolated or dead)</span>
  * <span style="color:green">Green: Rate of recovered population (which means: immune, isolated or dead)</span>
 
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Revision as of 17:34, 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 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)

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