Likelihood-Free Dynamical Survival Analysis Applied to the COVID-19 Epidemic in Ohio

The paper formulates the age-structured PDE system with nonlocal, implicit boundary conditions (eqs. (1), (3)–(5)) and converts those boundary conditions into a closed ODE “flow” system at s=0 (eq. (9)), then proves a short-time fixed-point/contraction result in a Banach space and the equivalence back to the original boundary conditions; see the PDE/BC setup , the derived boundary flows , the Lipschitz/structure bounds and fixed-point map FT with contraction (Lemma 1, Cor. 1) , and the boundary-equivalence argument via difference quotients . The candidate solution implements the same strategy: define a map T by freezing K(t)=∫β yI and the boundary flows, solve the linear transports by characteristics, show T maps a closed ball into itself and is a contraction for small h, then recover the implicit boundary relations at the fixed point. Minor omissions (e.g., not explicitly stating the continuity constraints (7) at the origin) do not affect the core argument, which otherwise matches the paper’s proof structure and conclusions .