Modelling remote epidemic transmission in Western Australia and implications for pandemic response

The uploaded paper defines the vulnerability index v(i) = Mi/MGero using the median time to first local transmission and supports its main claims empirically: remote communities are collectively highly vulnerable, behave like a strongly mixed virtual center, and shortest-path distance from Perth is the best simple predictor with some exceptions for smaller communities. These statements are consistent with the paper’s mobility rules (D(i,j) = B3/d(i,j) + r_i·r_j; biased traveller counts Tb(i); destination choice ∝ D(i,j)·max(P(i)/P(j),1)) and the SEIR parameters it uses. The candidate solution tries to turn these empirical observations into proofs; however, a key inequality is wrong: the map x ↦ 1 − (1 − p)^x is concave, so E[1 − (1 − p)^{N}] ≤ 1 − (1 − p)^{E[N]} (not ≥). This invalidates the claimed per-step hazard lower bound, the ensuing “median sandwich,” and the construction of a uniform β0 per-edge rate used in parts (a) and (b). Part (c) is qualitatively consistent with the paper’s ‘exceptions’ remark but relies on additional assumptions. Therefore, the paper’s empirical conclusions stand, but the model’s formal proof is flawed at a core step. Citations: definition of v(i) and empirical trends ; remote-communities-as-virtual-city narrative ; mobility rules D(i,j) and destination choice (eqs. (4),(6)) ; biased travel Tb(i) (eq. (5)) and SEIR parameters .