Fig. 5: Resistant population extinction under continuous fixed-dose treatment versus optimal adaptive therapy.

A Treatment of the single species sensitive cell population alone versus (B) treatment with the same doses of drug (r_d) in a mix of sensitive and resistant competing cells when β < 1/α and (C) when β > 1/α. D Phase plane when \(\beta < \frac{1}{\alpha }\) with the continuous adaptive δ = 0 separatrix shown in black with initial conditions under the line leading to resistant extinction (shaded grey). All initial conditions lead to resistant extinction under fixed-dose continuous therapy (shaded blue) with the minimum achievable tumor volume taken when r_d is set such that the intersection of the x and y nullclines occurs on the x-axis. E Phase planes when \(\beta > \frac{1}{\alpha }\) with the continuous adaptive δ = 0 separatrix shown in black with initial conditions under the line leading to resistant extinction (shaded grey). In the first phase plane, r_d is chosen such that for all initial conditions where continuous adaptive control leads to resistant population extinction, continuous fixed-dose treatment will also yield resistant species extinction with final tumor size smaller than A. F In the second phase plane, r_d is set such that the equilibrium under fixed-dose control for favorable initial conditions (shaded blue) is set to A. Simulation Parameters: (A–C), r_x = 0.04, r_y = 0.03, (x₀, y₀) = (0.3, 0.1) except (A) where y₀ = 0. In (B), α = 0.5 and β = 1.5. In (C), α = 0.9 and β = 2.