# Difference between revisions of "SIR model: swine flu"

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+ | 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. | ||

+ | * 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: | ||

+ | 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> | ||

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<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()"> | ||

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var beta = brd.createElement('slider', [[0,-0.4], [30,-0.4],[0,0.5,1]], {name:'β'}); | var beta = brd.createElement('slider', [[0,-0.4], [30,-0.4],[0,0.5,1]], {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],[0,0.166,1]], {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)"]); | ||

## Revision as of 12:09, 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[/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 2. 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]