# SIR model: swine flu

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The SIR model (see also Epidemiology: The SIR model) tries to predict influenza epidemics. Here, we try to model 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 $\displaystyle{ \gamma=1/7=0.1428 }$ 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 $\displaystyle{ R_0 }$ of the virus to be about $\displaystyle{ 2 }$. For the SIR model this means: the reproduction rate $\displaystyle{ R_0 }$ for influenza is equal to the infection rate of the strain ($\displaystyle{ \beta }$) multiplied by the duration of the infectious period ($\displaystyle{ 1/\gamma }$), i.e.
$\displaystyle{ \beta = R_0\cdot \gamma }$. Therefore, we set $\displaystyle{ \beta = 2\cdot 1/7 = 0.2857. }$ For the 1918–1919 pandemic $\displaystyle{ R_0 }$ is estimated to be between 2 and 3, whereas for the seasonal flu the range for $\displaystyle{ R_0 }$ is 0.9 to 2.1.
• We run the simulation for a population of 1 million people, where 1 person is infected initially, i.e. $\displaystyle{ s=1E{-6} }$.

Thus S(0) = 1, I(0) = 1.E-6, R(0) = 0. In [1] the mortality is estimated to be approximately 0.4 per cent. 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