# Difference between revisions of "Epidemiology: The SEIR model"

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− | var brd = JXG.JSXGraph.initBoard('box', { | + | var brd = JXG.JSXGraph.initBoard('box', {axis: true, boundingbox: [-4, 1.25, 114, -1.25]}); |

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− | function() {return "Day "+t+": infected="+ | + | function() {return "Day "+t+": infected="+(7900000*I.Y()).toFixed(1)+" recovered="+(7900000*R.Y()).toFixed(1);}]); |

## Latest revision as of 16:58, 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]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)