Figure 2
Observability signature for the Influenza model: Since there are nine parameters to be determined, there are nine columns in the matrix S(t 0, …, t N , θ). An SVD of this matrix then yields nine singular values σ 1, …, σ 9. These singular values are presented in the top graph on a logarithmic scale. Note the sudden gap between σ 8 and σ 9 of approximately 3.5 decades on the logarithmic scale, indicating a true zero for the last singular value and, hence, a possible lack of observability. The bottom graph clearly shows that the parameters q, T(0), I 1(0), and I 2(0) are involved in this total correlation, suggesting that there is an algebraic relationship between these parameters that deems the model un-identifiable.
