Oncolytic virotherapy for tumours following a Gompertz growth law

The paper’s Jacobian and characteristic polynomials at (K,0,0) and at the positive equilibrium match the candidate’s, yielding the same stability threshold γ=1 for the ineffective-treatment equilibrium (their Eq. (8)) and the same cubic for the partial-eradication equilibrium (their Eq. (9)) . The candidate then applies the standard cubic Routh–Hurwitz test in normalized form and gives an explicit Hopf condition via Δ(ξ)=a1a2−a3 with a1,a2,a3>0 and transversality from Δ′≠0, while the paper identifies Hopf (and GH) loci and bistability numerically with AUTO/XPPAUT and continuation plots . On the full-eradication equilibrium, the paper defers to numerics due to a singular Jacobian, whereas the candidate notes invariance of the U=0 face and linear decay of (I,V) there—an analytically valid complement to the paper’s discussion .