SIR model: swine flu: Difference between revisions
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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', [90,-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', [ | brd.createElement('text', [90,-0.4, "β: infection rate"]); | ||
var gamma = brd.createElement('slider', [[0,-0.5], [60,-0.5],[0,0.1428,1]], {name:'γ'}); | var gamma = brd.createElement('slider', [[0,-0.5], [60,-0.5],[0,0.1428,1]], {name:'γ'}); | ||
brd.createElement('text', [ | brd.createElement('text', [90,-0.5, "γ: recovery rate = 1/(days of infection)"]); | ||
var t = 0; // global | var t = 0; // global | ||
Revision as of 11:32, 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]\displaystyle{ \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]\displaystyle{ R_0 }[/math] of the virus to be about [math]\displaystyle{ 2 }[/math]. For the SIR model this means: the reproduction rate [math]\displaystyle{ R_0 }[/math] for influenza is equal to the infection rate of the strain ([math]\displaystyle{ \beta }[/math]) multiplied by the duration of the infectious period ([math]\displaystyle{ 1/\gamma }[/math]), i.e.
- [math]\displaystyle{ \beta = R_0\cdot \gamma }[/math]. Therefore, we set the :[math]\displaystyle{ \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]\displaystyle{ s=1E{-6} }[/math].
Thus S(0) = 1, I(0) = 1.E-6, R(0) = 0
