Epidemiology: The SEIR model: Difference between revisions

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<jsxgraph width="700" height="600" box="box">
var brd = JXG.JSXGraph.initBoard('box', {originX: 20, axis: true, originY: 300, unitX: 6, unitY: 250});
var brd = JXG.JSXGraph.initBoard('box', {axis: true, boundingbox: [-4, 1.25, 114, -1.25]});

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brd.createElement('text', [40,-0.2,  
brd.createElement('text', [40,-0.2,  
         function() {return "Day "+t+": infected="+brd.round(7900000*I.Y(),1)+" recovered="+brd.round(7900000*R.Y(),1);}]);
         function() {return "Day "+t+": infected="+(7900000*I.Y()).toFixed(1)+" recovered="+(7900000*R.Y()).toFixed(1);}]);

Latest revision as of 14:58, 20 February 2013

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)

See also