Epidemiology: The SEIR model: Difference between revisions

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The lines in the JSXGraph-simulation below have the following meaning:
The lines in the JSXGraph-simulation below have the following meaning:
  * <span style="color:Blue">Blue: Rate of susceptible population</span>
  * <span style="color:Blue">Blue: Rate of susceptible population</span>
  * <span style="color:yellow">Vellow: Rate of exposed population</span>
  * <span style="color:black">Black: Rate of exposed population</span>
  * <span style="color:red">Red: Rate of infectious population</span>
  * <span style="color:red">Red: Rate of infectious population</span>
  * <span style="color:green">Green: Rate of recovered population (which means: immune, isolated or dead)
  * <span style="color:green">Green: Rate of recovered population (which means: immune, isolated or dead)
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var S = brd.createElement('turtle',[],{strokeColor:'blue',strokeWidth:3});
var S = brd.createElement('turtle',[],{strokeColor:'blue',strokeWidth:3});
var E = brd.createElement('turtle',[],{strokeColor:'yellow',strokeWidth:3});
var E = brd.createElement('turtle',[],{strokeColor:'black',strokeWidth:3});
var I = brd.createElement('turtle',[],{strokeColor:'red',strokeWidth:3});
var I = brd.createElement('turtle',[],{strokeColor:'red',strokeWidth:3});
var R = brd.createElement('turtle',[],{strokeColor:'green',strokeWidth:3});
var R = brd.createElement('turtle',[],{strokeColor:'green',strokeWidth:3});

Revision as of 08:04, 27 April 2009

For many important infections there is a significant period of time during which the individual has been infected but is not yet infectious himself. During this latent period the individual is in compartment E (for exposed).

Assuming that the period of staying in the latent state is a random variable with exponential distribution with parameter a (i.e. the average latent period is [math]\displaystyle{ a^{-1} }[/math]), and also assuming the presence of vital dynamics with birth rate equal to death rate, we have the model:

[math]\displaystyle{ \frac{dS}{dt} = \mu N - \mu S - \beta \frac{I}{N} S }[/math]
[math]\displaystyle{ \frac{dE}{dt} = \beta \frac{I}{N} S - (\mu +a ) E }[/math]
[math]\displaystyle{ \frac{dI}{dt} = a E - (\gamma +\mu ) I }[/math]
[math]\displaystyle{ \frac{dR}{dt} = \gamma I - \mu R. }[/math]

Of course, we have that [math]\displaystyle{ S+E+I+R=N }[/math].

The lines in the JSXGraph-simulation below have the following meaning:

* Blue: Rate of susceptible population
* Black: Rate of exposed population
* Red: Rate of infectious population
* Green: Rate of recovered population (which means: immune, isolated or dead)