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

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var s = brd.createElement('slider', [[0,-0.3], [10,-0.3],[0,0.03,1]], {name:'s'}); | var s = brd.createElement('slider', [[0,-0.3], [10,-0.3],[0,0.03,1]], {name:'s'}); | ||

− | brd.createElement('text', [12,-0. | + | brd.createElement('text', [12,-0.3, "initially infected population rate"]); |

var beta = brd.createElement('slider', [[0,-0.4], [10,-0.4],[0,0.5,1]], {name:'β'}); | var beta = brd.createElement('slider', [[0,-0.4], [10,-0.4],[0,0.5,1]], {name:'β'}); | ||

− | brd.createElement('text', [12,-0. | + | brd.createElement('text', [12,-0.4, "β: infection rate"]); |

var gamma = brd.createElement('slider', [[0,-0.5], [10,-0.5],[0,0.3,1]], {name:'γ'}); | var gamma = brd.createElement('slider', [[0,-0.5], [10,-0.5],[0,0.3,1]], {name:'γ'}); | ||

− | brd.createElement('text', [12,-0. | + | brd.createElement('text', [12,-0.5, "γ: recovery rate"]); |

− | brd.createElement('text', [12,-0. | + | brd.createElement('text', [12,-0.2, |

function() {return "S(t)="+brd.round(S.pos[1],3) +", I(t)="+brd.round(I.pos[1],3) +", R(t)="+brd.round(R.pos[1],3);}]); | function() {return "S(t)="+brd.round(S.pos[1],3) +", I(t)="+brd.round(I.pos[1],3) +", R(t)="+brd.round(R.pos[1],3);}]); | ||

## Revision as of 19:47, 21 January 2009

Simulation of differential equations with turtle graphics using JSXGraph.

### SIR model without vital dynamics

A single epidemic outbreak is usually far more rapid than the vital dynamics of a population, thus, if the aim is to study the immediate consequences of a single epidemic, one may neglect the birth-death processes. In this case the SIR system described above can be expressed by the following set of differential equations:

- [math] \frac{dS}{dt} = - \beta I S [/math]

- [math] \frac{dR}{dt} = \gamma I [/math]

- [math] \frac{dI}{dt} = -(dS+dR) [/math]

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

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