On parameter identifiability in network-based epidemic models

The paper and the model reach the same conclusions: (i) in the well-mixed SIR ODE only β=τn is identifiable (strong unidentifiability), (ii) in the pairwise SIR with κ=(n−1)/n one reduces the inference to a single scalar equation in n where the function f(n) is nearly constant, yielding weak unidentifiability, and (iii) in the EBCM on Poisson(n), eliminating τ gives λ+γ=γq (n−1)/(n−q) with q=ln(s∞)/(s∞−1)>1, and f(n) decreases to 1, again implying weak unidentifiability. The model reproduces the paper’s reductions and asymptotics, and (for EBCM) correctly proves monotonicity on (2,∞) under q<2. Minor differences are present in exposition and in how “infinite measure” is justified (line vs. band), but the mathematical content agrees.