Suppose = 1 in the basic disease model dI/dt = I(1 - I) - I. Graph the two equilibria as functions of for

Suppose μ = 1 in the basic disease model dI/dt = αI(1 - I) - μI. Graph the two equilibria as functions of α for values of a between 0 and 2, using a solid line when an equilibrium is stable and a dashed line when an equilibrium is unstable. Even though they do not make biological sense, include negative values of the equilibria on your graph. You should find a transcritical bifurcation at α = 1.
Exercises 17-20 show how the number and stability of equilibria can change when a parameter changes. Often, bifurcations have important biological applications, and bifurcation diagrams help in explaining how the dynamics of a system can suddenly change when a parameter changes only slightly. In each case, graph the equilibria against the parameter value, using a solid line when an equilibrium is stable and a dashed line when an equilibrium is unstable to draw the bifurcation diagram.