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

Figure 6

The phase spaces at different equilibria where stable steady states [•], unstable steady states [○], stable manifold [- - -], unstable manifold [⋯], and initial conditions [+], exist. (with immunotherapy with both ACI and IL-2, see Table 1 and 𝑠₁=40, 𝑠₂=10.).

(a) Tumor-free equilibrium (𝑟₂=1 and 𝛼=5∗10⁻³)

(b) One persistent-tumor equilibrium with a stable limit cycle (𝑟₂=1 and 𝛼=2∗10⁻⁵)

(c) One persistent-tumor equilibrium at little 𝛼 (𝑟₂=1 and 𝛼=2.7∗10⁻⁵)

(d) One persistent-tumor equilibrium (𝑟₂=1 and 𝛼=2∗10⁻³)

(e) Three persistent-tumor equilibria with a stable limit cycle (𝑟₂=0.5 and 𝛼=1.8∗10⁻⁵)

(f) Three persistent-tumor equilibria (𝑟₂=1 and 𝛼=4∗10⁻⁵)