Getting certain derivative value from a system of differential equations

Question

I have the following differential equations system:

$\frac{dS}{dt} = -0.001SI$

and

$\frac{dI}{dt} = 0.001SI - 0.3I$

How do I retrieve the value of $\frac{dI}{dS}$ ? I know its supposed to be $\frac{dI}{dS} = -1 + \frac{300}{S}$

Answer 1

$$\dfrac{dI}{dS} = \dfrac{dI/dt}{dS/dt} = \dfrac{0.001 SI -0.3I}{-0.001SI}= -1 + \dfrac{300}{S}$$

Answer 2

Just divide the second of equations by the first to elminate $t$. That simple.