The figure above shows infections being driven to zero when the reproduction number is below one, indicating the desired stability of the system.
For our stability analysis, we proved that when the effective control reproduction number is below one, the system is indeed stable as expected. We did this by using both the disease free equilibrium state and the endemic equilibrium state. Essentially, we showed that the eigenvalues of the system are stable when the reproduction number is below one. This is crucial to showing that our model is sound and that the reproduction number can actually be used to make conclusions about the nature of this epidemic.