SIR model: swine flu
From JSXGraph WikiJump to navigationJump to search
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