SIR model: swine flu

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 $\gamma=1/7=0.1428$ 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 $R_0$ of the virus to be about $2$. For the SIR model this means: the reproduction rate $R_0$ for influenza is equal to the infection rate of the strain ($\beta$) multiplied by the duration of the infectious period ($1/\gamma$), i.e.
$\beta = R_0\cdot \gamma$. Therefore, we set $\beta = 2\cdot 1/7 = 0.2857.$ For the 1918–1919 pandemic $R_0$ is estimated to be between 2 and 3, whereas for the seasonal flu the range for $R_0$ 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. $s=1E{-6}$.

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