A Linear Dynamical Perspective on Epidemiology: Interplay Between Early COVID-19 Outbreak and Human Mobility

The paper and the candidate solution both formulate an HDMDc pipeline that (i) constructs delay-embedded snapshots X,X′, (ii) builds control inputs Υ from Google mobility via cross-county min–max scaling with a weight w, (iii) estimates A,B by least squares from the stacked regressor Ω, and (iv) evaluates rolling forecasts at 2–4 week horizons, including a 14-day leader–follower shift of mobility and an R(t) back-out via a renewal equation. The paper documents the same design choices and empirical claims: the control construction uk,i := w(pk,i−pmin,i)/(pmax,i−pmin,i) (eq. 10), a 14-day shift improving errors versus unshifted and no-mobility baselines, and MAPE levels <5% (two-week) and <10% (three-week), with larger delay embeddings improving average 4-week performance but hurting a few counties; it also reports average R(t) error ≈10.63% and worst-case discrepancy ≈0.2, all matching the model’s outline and examples (e.g., h=29,w=200 for 2 weeks; h=42,w=400 for 3 weeks) . Mathematically, both adopt X′ = AX + BΥ and the standard SVD/pseudoinverse solution; however, the paper’s printed formula for extracting A and B (its eq. (8)) is dimensionally inconsistent and should be corrected to the block-partitioned pseudoinverse form used by the model (Â = X′VΣ^{-1}U_X^*, B̂ = X′VΣ^{-1}U_Υ^*) . Aside from these notational/dimensional slips (and a likely “3–4 days” typo rendered as “34 days”), the arguments and empirical protocol align. Overall: same method, same logic, same conclusions; the model states the estimator more precisely, while the paper contains minor—but correctable—presentation errors.