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sir1b (controlled SIR)

$\displaystyle \frac{dS}{dt}$ $\displaystyle =-r(t) S(t) I(t)$    
$\displaystyle \frac{dI}{dt}$ $\displaystyle =r(t) S(t) I(t)-a(t) I(t)$    
$\displaystyle \frac{dR}{dt}$ $\displaystyle =a(t) I(t)$    

with $ r(t)=r_1$ and $ a(t)=a_1$ for $ t<\tau$, and $ r(t)=r_2$ and $ a(t)=a_2$ for $ t>\tau$.

Figure 4.9: Infected and removed
\includegraphics[width=10cm]{images/sir1b.eps}


Nicolas Bacaer 2004-06-18