Observability, Identifiability and Epidemiology A survey

The paper’s Theorem 3.1 states exactly the claims at issue: for the SIR system with observation y = k I, the augmented system is neither observable nor identifiable; the identifiable functions are {k I, β/(k N), β S/N, γ} (equivalently {k S, k I, γ, β/(k N)}); if N is known and k = 1 or k = γ, then the system is observable and identifiable; and if k = γ (with N unknown), then S, I, γ, and β/N are identifiable. These statements and their scope match the candidate solution precisely . The paper derives an input–output differential relation (displayed with a minor typographical variant) and also uses an ORC/Jacobian calculation to certify non-observability of the augmented system . The candidate solution proves non-observability via an explicit scaling symmetry and identifies parameters by eliminating the state to obtain the same input–output equation and a clean monotonicity argument (α̇ = −c α y < 0) to rule out degeneracies; this differs in style but not substance from the paper’s approach. A small display-level typo in the paper’s input–output relation (ẏ ÿ vs. y ÿ) does not affect conclusions and is readily reconciled by the algebra shown in the paper and in the candidate solution .