6.2 Determining stability of an equilbrium solution

The picture of the phase plane with the nullcline qualitatively tells us about the stability of an equilibrium point. Once of the equilibrium solutions is at the origin \((S,I)=(0,0)\). As before we want to investigate if the equilibrium solution is stable or unstable.

Figure 6.4 zooms in the phaseplane at the equilibrium solution at \(S=0\), \(I=0\):

Figure 6.4: Zoomed in view of the phaseplane for Equation (6.2)

As you can see the arrows appear to be pointing into and towards the equilibrium solution. So we would classify this equilbrium solution as stable.