Dynamical compensation and structural unidentifiability in the βIG model.

The first row reproduces the last row of Fig 2 and illustrates the phenomenon of dynamical compensation: after the system has adapted to the new value of s_i, the time-evolution of the glucose concentration (G) for the new value of (s_i/2) is the same as it was with the old value before adaptation (s_i). The second row illustrates the phenomenon of structural unidentifiability: without the need for any adaptation, the time-evolution of the glucose concentration (G) is the same for any value of the parameter s_i, as long as any deviations from the original value are compensated by changes in the parameter p. Note that, since the upper and lower plots of G are identical, if glucose is the only measured quantity both phenomena cannot be distinguished. However, the behaviour of the other state variables (I, β) can be very different, as can be noticed from the third and fourth columns.