Difference between revisions of "Epidemiology: The SEIR model"

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var gamma = brd.createElement('slider', [[0,-0.5], [30,-0.5],[0,0.3,1]], {name:'γ'});
 
var gamma = brd.createElement('slider', [[0,-0.5], [30,-0.5],[0,0.3,1]], {name:'γ'});
 
var mu = brd.createElement('slider', [[0,-0.6], [30,-0.6],[0,0.0,1]], {name:'μ'});
 
var mu = brd.createElement('slider', [[0,-0.6], [30,-0.6],[0,0.0,1]], {name:'μ'});
var a = brd.createElement('slider', [[0,-0.7], [30,-0.7],[0,0.0,1]], {name:'a'});
+
var a = brd.createElement('slider', [[0,-0.7], [30,-0.7],[0,1.0,1]], {name:'a'});
  
 
brd.createElement('text', [40,-0.3, "initially infected population rate (on load: I(0)=1.27E-6)"]);
 
brd.createElement('text', [40,-0.3, "initially infected population rate (on load: I(0)=1.27E-6)"]);

Revision as of 09:03, 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]a^{-1}[/math]), and also assuming the presence of vital dynamics with birth rate equal to death rate, we have the model:

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

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

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

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