# 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. | + | The SIR model,see also [[Epidemiology: 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=0.1428</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 <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. | * 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. | ||

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* We run the simulation for a population of 1 million people, where 1 person is infected initially, i.e. <math>s=1E{-6}</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 | Thus S(0) = 1, I(0) = 1.E-6, R(0) = 0 | ||

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

+ | * <span style="color:Blue">Blue: Rate of susceptible population</span> | ||

+ | * <span style="color:red">Red: Rate of infected population</span> | ||

+ | * <span style="color:green">Green: Rate of recovered population | ||

<html> | <html> | ||

<form><input type="button" value="clear and run a simulation of 200 days" onClick="clearturtle();run()"> | <form><input type="button" value="clear and run a simulation of 200 days" onClick="clearturtle();run()"> | ||

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var s = brd.createElement('slider', [[0,-0.3], [60,-0.3],[0,1E-6,1]], {name:'s'}); | var s = brd.createElement('slider', [[0,-0.3], [60,-0.3],[0,1E-6,1]], {name:'s'}); | ||

− | brd.createElement('text', [ | + | brd.createElement('text', [120,-0.3, "initially infected population rate"]); |

var beta = brd.createElement('slider', [[0,-0.4], [60,-0.4],[0,0.2857,1]], {name:'β'}); | var beta = brd.createElement('slider', [[0,-0.4], [60,-0.4],[0,0.2857,1]], {name:'β'}); | ||

brd.createElement('text', [90,-0.4, "β: infection rate"]); | brd.createElement('text', [90,-0.4, "β: infection rate"]); |

## Revision as of 13:33, 10 August 2009

The SIR model,see also Epidemiology: 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 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