SIR model: swine flu

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 }[/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 2. 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]

0,0

–o+←↓↑→

s = 0.03

initially infected population rate

β = 0.50

β: infection rate

γ = 0.17

γ: recovery rate = 1/(days of infection)