SIR model: 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 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 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