Figure 7

System responses to therapy. Three trios of curves (calculated from solutions of (11)-(15), using (27)) showing how the tumour burden, p _tot , varies after a single bolus of chemotherapy (black dashed lines) and 4 boluses of chemotherapy (red dotted lines). Here time, t, represents time since therapy was initialised. (A) In this case, before therapy is applied, the dynamics behind the invading front evolve to a stable equilibrium. Both a single bolus and multiple boluses decrease tumour burden relative to untreated control (solid line). This persists even during the recovery phase, when the effects of the therapy wane and the tumour starts to regrow. Multiple boluses are clearly more effective than a single bolus. (B) When in the absence of therapy tumour invasion results in the development of regular oscillations (solid line), the therapies induce oscillations of larger amplitude during the regrowth phase. Multiple boluses are slightly more effective than a single bolus. (C) When irregular oscillations occur in the absence of therapy (solid line), chemotherapies lead to an increase in the amplitude of these oscillations during the recovery phase. Multiple boluses do not improve the therapeutic response. Key: solid lines: no therapy; black dashed lines: single bolus; red dotted lines: 4 boluses (each separated by ten time units). Parameter values: as in Figure 6 with d _c = 2.0 × 10⁴, D _c = 1.6 × 10⁴, h _c = 1.3 × 10³, k = 0.9 and K _c = 0.05.