ON EXISTENCE OF TRAVELING WAVE OF AN HBV INFECTION DYNAMICS MODEL: A NOVEL APPROACH

The paper reduces the PDE to the 5D traveling-wave ODE (5.3), identifies E1* and E2*, and then applies Gershgorin discs to a 4×4 subblock of the Jacobian at E1*. From the disjointness of discs under (i)–(iii), it infers at least one positive eigenvalue and concludes a heteroclinic traveling wave exists; however, it never analyzes E2*, nor does it supply any invariant-set/trapping, comparison, or manifold-intersection argument linking local spectra to a global connection, and even defines a heteroclinic path for a linear system with two equilibria (which is impossible) . The model’s solution outlines a conventional invariant-region/Schur-complement/Routh–Hurwitz/Ważewski program, but key steps are incorrect or unproven: the crucial scalar inequality for u4 has the inequality sign reversed, several spectral sign claims require extra size conditions beyond (i)–(iii), and the E2* cubic’s constant-term sign is misread, undermining the stated unstable/stable manifold dimensions. Hence, both the paper’s argument and the model’s Phase-2 proof are incomplete.