Difference between revisions of "SIR model: swine flu"
From JSXGraph Wiki
Jump to navigationJump to searchA WASSERMANN (talk | contribs) |
A WASSERMANN (talk | contribs) |
||
| Line 1: | Line 1: | ||
The SIR model tries to model influenza epidemics. Here, we try to medel the spreading of the swine flu. | The SIR model tries to model influenza epidemics. Here, we try to medel the spreading of the swine flu. | ||
| − | * According to the [http://www.cdc.gov/ CDC Centers of Disease Control and Prevention]: "Adults shed influenza virus from the day before symptoms begin through 5-10 days after illness onset. However, the amount of virus shed, and presumably infectivity, decreases rapidly by 3-5 days after onset in an experimental human infection model." So, here we set <math>\gamma=1/7</math> as the recovery rate. This means, on average an infected person sheds the virus for 7 days. | + | * According to the [http://www.cdc.gov/ CDC Centers of Disease Control and Prevention]: "Adults shed influenza virus from the day before symptoms begin through 5-10 days after illness onset. However, the amount of virus shed, and presumably infectivity, decreases rapidly by 3-5 days after onset in an experimental human infection model." So, here we set <math>\gamma=1/7=0.1428</math> as the recovery rate. This means, on average an infected person sheds the virus for 7 days. |
| − | * In [http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=2715422 Modeling influenza epidemics and pandemics: insights into the future of swine flu (H1N1)] the authors estimate the reproduction rate <math>R_0</math> of the virus to be about 2. For the SIR model this means: | + | * In [http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=2715422 Modeling influenza epidemics and pandemics: insights into the future of swine flu (H1N1)] the authors estimate the reproduction rate <math>R_0</math> of the virus to be about <math>2</math>. For the SIR model this means: the reproduction rate <math>R_0</math> for influenza is equal to the infection rate of the strain (<math>\beta</math>) multiplied by the duration of the infectious period (<math>1/\gamma</math>), i.e. |
| − | the reproduction rate <math>R_0</math> for influenza is equal to the infection rate of the strain (<math>\beta</math>) multiplied by the duration of the infectious period (<math>1/\gamma</math>), i.e. | + | :<math>\beta = R_0\cdot \gamma</math>. Therefore, we set the :<math>\beta = 2\cdot 1/7 = 0.2857</math> |
| − | :<math>\beta = R_0\cdot \gamma</math> | + | * We run the simulation for a population of 1 million people, where 1 person is infected initially, i.e. <math>s= 1E-6</math>. |
| − | + | Thus S(0) = 1, I(0) = 1.E-6, R(0) = 0 | |
| − | |||
<html> | <html> | ||
<form><input type="button" value="clear and run a simulation of 100 days" onClick="clearturtle();run()"> | <form><input type="button" value="clear and run a simulation of 100 days" onClick="clearturtle();run()"> | ||
| Line 21: | Line 20: | ||
var yaxis = brd.createElement('axis', [[0,0], [0,1]], {}); | var yaxis = brd.createElement('axis', [[0,0], [0,1]], {}); | ||
| − | var s = brd.createElement('slider', [[0,-0.3], [30,-0.3],[0, | + | var s = brd.createElement('slider', [[0,-0.3], [30,-0.3],[0,1E-6,1]], {name:'s'}); |
brd.createElement('text', [40,-0.3, "initially infected population rate"]); | brd.createElement('text', [40,-0.3, "initially infected population rate"]); | ||
| − | var beta = brd.createElement('slider', [[0,-0.4], [30,-0.4],[0,0. | + | var beta = brd.createElement('slider', [[0,-0.4], [30,-0.4],[0,0.2857,1]], {name:'β'}); |
brd.createElement('text', [40,-0.4, "β: infection rate"]); | brd.createElement('text', [40,-0.4, "β: infection rate"]); | ||
| − | var gamma = brd.createElement('slider', [[0,-0.5], [30,-0.5],[0,0. | + | var gamma = brd.createElement('slider', [[0,-0.5], [30,-0.5],[0,0.1428,1]], {name:'γ'}); |
brd.createElement('text', [40,-0.5, "γ: recovery rate = 1/(days of infection)"]); | brd.createElement('text', [40,-0.5, "γ: recovery rate = 1/(days of infection)"]); | ||
| Line 31: | Line 30: | ||
brd.createElement('text', [40,-0.2, | brd.createElement('text', [40,-0.2, | ||
| − | function() {return "Day "+t+": infected="+brd.round( | + | function() {return "Day "+t+": infected="+brd.round(1000000*I.Y(),1)+" recovered="+brd.round(1000000*R.Y(),1);}]); |
S.hideTurtle(); | S.hideTurtle(); | ||
Revision as of 13:29, 10 August 2009
The SIR model tries to model influenza epidemics. Here, we try to medel the spreading of the swine flu.
- According to the CDC Centers of Disease Control and Prevention: "Adults shed influenza virus from the day before symptoms begin through 5-10 days after illness onset. However, the amount of virus shed, and presumably infectivity, decreases rapidly by 3-5 days after onset in an experimental human infection model." So, here we set [math]\gamma=1/7=0.1428[/math] as the recovery rate. This means, on average an infected person sheds the virus for 7 days.
- In Modeling influenza epidemics and pandemics: insights into the future of swine flu (H1N1) the authors estimate the reproduction rate [math]R_0[/math] of the virus to be about [math]2[/math]. For the SIR model this means: the reproduction rate [math]R_0[/math] for influenza is equal to the infection rate of the strain ([math]\beta[/math]) multiplied by the duration of the infectious period ([math]1/\gamma[/math]), i.e.
- [math]\beta = R_0\cdot \gamma[/math]. Therefore, we set the :[math]\beta = 2\cdot 1/7 = 0.2857[/math]
- We run the simulation for a population of 1 million people, where 1 person is infected initially, i.e. [math]s= 1E-6[/math].
Thus S(0) = 1, I(0) = 1.E-6, R(0) = 0
