Qualitative and Computational Analysis of a Mathematical Model for Tumor-Immune Interactions

Figure 4

shows the bifurcation diagrams for the bilinear model (2.5) for the parameter 𝛼: [—] represents the stable equilibrium, [- - -] represents the unstable equilibrium, [⋯] is the stable limit cycles, while [∘] is the saddle node bifurcation. [•] is the transcritical bifurcation and [□] the supercritical Hopf bifurcation. The values of parameters are given in Table 1.

(a) No Treatment Case, 𝑠₁=𝑠₂=0

(b) Interleukin-2 Case 𝑠₁=0, 𝑠₂=10

(c) Adoptive cellular immunotherapy case, 𝑠₁=40, 𝑠₂=0

(d) Small interval of 𝛼 for ACI Case, 𝑠₁=40, 𝑠₂=0

(e) Immunotherapy with both ACI and IL-2 𝑠₁=40, 𝑠₂=10

(f) Small interval of 𝛼 for immunotherapy with both ACI and IL-2 case, 𝑠₁=40, 𝑠₂=10