Cancer model with moving extinction threshold reproduces real cancer data

The paper’s condition for the existence of two positive equilibria in Model 2 (its fold threshold for s) is derived by solving f(x)=0 and f′(x)=0 and then eliminating x, but the printed result s = (1/(μν))(νr/(ν+1))^{ν+1} has the wrong μ dependence and an extra 1/ν. The correct threshold is s* = [(νr)/(ν+1)]^{ν+1} μ^{−ν}, obtained by evaluating the concave maximum of g(x)=νrx−νμx^{(ν+1)/ν}. The candidate solution derives the correct g_max and all subsequent conclusions (number and stability of equilibria) follow correctly. The discrete-time moving-threshold derivation and its large-ν/log-linear approximation match the paper’s formulas exactly.