Fig. 2: Model dynamics.
From: Effective dose window for containing tumor burden under tolerable level
The upper panel (a) shows the bifurcation diagram. Ktol is the tolerable tumor volume (TTV), which is also assumed to be the threshold tumor burden that determines tumor progression. The vertical gray dotted lines divide the domain into three parts, showing the equilibria for Cases I, II, and III. The solid orange line shows the stable R-only equilibrium and the solid blue line shows the stable S-only equilibrium. The dashed blue line indicates an unstable S-only equilibrium. The dash-dot blue and orange lines indicate the S-cell and R-cell populations, respectively, in the unstable coexistence equilibrium. The solid black line represents the tolerable tumor volume and corresponding drug-induced death rate. The horizontal double arrow indicates the EDW. The lower panel shows the phase diagrams for cases III (b), II (c), and I (d) (from left to right). Triangular regions indicate the phase space. The dotted blue and orange lines represent the S- and R- nullclines, respectively. The dashed lines with different shades of gray are the trajectories starting from different points in the phase space where empty dots indicate initial conditions. The solid black curve (b) shows the separatrix in case III. The orange-filled dots show the stable R-only equilibrium in all the cases. The blue-filled dot in Case III indicates a stable S-only equilibrium. The blue empty dot shows the unstable S-only equilibrium in Case II. It is observed that the trajectories starting from the same three points (gray empty dots) evolve in a different manner as δ changes. The assumed parameter values for the above diagram are r = 0.02, c = 3, K = 1000, and Ktol = 500, and the initial conditions for the phase portraits are (S(0), R(0)) = (800, 190), (200, 200), and (450, 500).
