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

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var R = brd.createElement('turtle',[],{strokeColor:'green',strokeWidth:3}); | var R = brd.createElement('turtle',[],{strokeColor:'green',strokeWidth:3}); | ||

+ | var xaxis = brd.createElement('axis', [[0,0], [1,0]], {}); | ||

+ | var yaxis = brd.createElement('axis', [[0,0], [0,1]], {}); | ||

+ | |||

+ | var s = brd.createElement('slider', [[0,-0.5], [10,-0.5],[0,0.03,1]], {name:'s'}); | ||

+ | brd.createElement('text', [12,-0.5, "initially infected population rate"]); | ||

+ | var beta = brd.createElement('slider', [[0,-0.6], [10,-0.6],[0,0.5,1]], {name:'β'}); | ||

+ | brd.createElement('text', [12,-0.6, "β: infection rate"]); | ||

+ | var gamma = brd.createElement('slider', [[0,-0.7], [10,-0.7],[0,0.3,1]], {name:'γ'}); | ||

+ | brd.createElement('text', [12,-0.7, "γ: recovery rate"]); | ||

+ | brd.createElement('text', [12,-0.4, | ||

+ | 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);}]); | ||

+ | |||

+ | S.hideTurtle(); | ||

+ | I.hideTurtle(); | ||

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</script> | </script> | ||

</html> | </html> |

## Revision as of 19:40, 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)