Analytical Mechanics Allows Novel Vistas on Mathematical Epidemic Dynamics Modelling

The paper explicitly introduces the time reparameterization τ with dτ/dt = S I, derives I° = β − γ/S and S° = −β, identifies the Hamiltonian H(Z) = β(I + S) − γ ln S yielding Z° = J ∂ZH, and reduces the dynamics to the scalar ODE I°° = −R0(β − I°)^2; these are given verbatim in the text (see the development around the reparameterized system, its Hamiltonian form, and Eq. (7) for the scalar ODE) . For the logarithmic coordinate change i = ln I, s = ln S, the paper derives i• = βS − γ, s• = −βI, presents the Hamiltonian h(z) = β(e^i + e^s) − γ s with z• = j ∂zh, and the scalar ODE i•• = −β I(i) [i• + γ] (Eqs. (47), (49), (51)–(53)) . The candidate solution reproduces exactly these steps, formulas, and conclusions. A minor improvement in the candidate is an explicit statement of domain assumptions (β>0, γ>0, and S, I > 0) ensuring that the time rescaling and logarithms are well-defined; these are implicitly assumed but not made explicit in the paper’s prose. Overall, both are correct and essentially identical in method and result.