Finding nullclines for ODEs I am getting confused on how to find the vertical and horizontal nullclines for a set of ODEs. I understand I have to set them to 0, and then solve but whether I rearrange/solve for $x$ or $y$ (in this case $s$ and $i$) is what's confusing me. 
For example: I am trying to draw a s-i plane for (susceptible-infected) the following two ODEs:
$$ds/dt = -0.7si$$
$$di/dt = 0.7si - 0.2i$$
For the vertical nullcine I set $ds/dt = 0$:
$$0=-0.7si $$
For the horizontal nullcline I set $di/dt=0$:
$$0=0.7si-0.2i$$
In each case, what am I rearranging for? Do I have to get $i$ in terms of $s$? Or $s$ in terms of $i$?

The equation $-0.7 si = 0$ is equivalent to $s=0$ or $i=0$. So the nullcline for $s$ will just be the union of the two straight lines whose equations are $s=0$ and $i=0$.
Can you now find the nullcline for $i$ similarly? Write the equation as $i(0.7s-0.2)=0$.
