Computation of COVID-19 epidemiological data in Hungary using dynamic model inversion

The paper’s PIH-subsystem, observer design, and RLS-based β-estimation are reproduced almost verbatim in the candidate solution. The candidate correctly shows CB=0, CAB=0, CA^2B>0 and r=3; constructs the same UIO with H=B(O3B)†, F=A−HO3A−K1O3, K=K1+FH; recovers A,R,D and S via (1e),(1g),(1h) and conservation; and uses the identical forward-Euler regression πk=ϕkβk with the same scalar-RLS update to estimate β, then R0 and Rc via Eqs. (2)–(3). These steps match Sections 3.2–3.4 and formulas (6)–(8), (15)–(21), (22)–(24) in the paper, including the derivative-based unknown-input recovery via y^{(3)} and CA^2B (cf. equations (15)–(20) and discussion around (17)–(21) in 3.3). Minor practical assumptions (noise smoothing, persistent excitation) are implicit but standard and also noted by the paper.