Difference between revisions of "Epidemiology: The SEIR model"
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+ | ===See also=== | ||
+ | * [[Epidemiology: The SIR model]] | ||
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+ | ===References=== | ||
+ | * [http://en.wikipedia.org/wiki/Compartmental_models_in_epidemiology http://en.wikipedia.org/wiki/Compartmental_models_in_epidemiology] | ||
+ | |||
+ | [[Category:Examples]] | ||
+ | [[Category:Turtle Graphics]] | ||
+ | [[Category:Calculus]] |
Revision as of 10:08, 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 * Black: Rate of exposed population * Red: Rate of infectious population * Green: Rate of recovered population (which means: immune, isolated or dead)