Epidemiology: The SIR model: Difference between revisions

From JSXGraph Wiki
No edit summary
 
No edit summary
Line 4: Line 4:
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:
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:


    \frac{dS}{dt} = - \beta I S    
:<math> \frac{dS}{dt} = - \beta I S </math>
   
    \frac{dI}{dt} = \beta I S - \nu I


    \frac{dR}{dt} = \nu I
:<math> \frac{dR}{dt} = \gamma I </math>
 
:<math> \frac{dI}{dt} = -(dS+dR) </math>

Revision as of 17:32, 21 January 2009

Simulation of differential equations with turtle graphics.

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]