Answer
$80.16$ and $r=0$
Work Step by Step
I. As per the given problem, we have:
$r=kx(P-x)$
Here, $k$ is defined as constant of proportionality
when the length gets doubled then we have
$r_{10}=k(10)(5000-10) \implies 49900k$
and $r_{1000}=k(1000)(5000-1000) \implies 4000000k$
Plug the given data in the above expression, we get
$\dfrac{r_{10000}}{r_{10}}=\dfrac{4000000k}{49900k}=80.16$
II. When all the people are infected.there will be no infection spread .
Then, we have $x=P$
This gives: $r=kP(P-P)=0$