Journal of Applied Mathematics / 2012 / Article / Fig 6

Research Article

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

Figure 6

The phase spaces at different equilibria where stable steady states [β€’], unstable steady states [β—‹], stable manifold [- - -], unstable manifold [β‹―], and initial conditions [+], exist. (with immunotherapy with both ACI and IL-2, see Table 1 and 𝑠 1 = 4 0 , 𝑠 2 = 1 0 .).
475720.fig.006a
(a) Tumor-free equilibrium ( π‘Ÿ 2 = 1 and 𝛼 = 5 βˆ— 1 0 βˆ’ 3 )
475720.fig.006b
(b) One persistent-tumor equilibrium with a stable limit cycle ( π‘Ÿ 2 = 1 and 𝛼 = 2 βˆ— 1 0 βˆ’ 5 )
475720.fig.006c
(c) One persistent-tumor equilibrium at little 𝛼 ( π‘Ÿ 2 = 1 and 𝛼 = 2 . 7 βˆ— 1 0 βˆ’ 5 )
475720.fig.006d
(d) One persistent-tumor equilibrium ( π‘Ÿ 2 = 1 and 𝛼 = 2 βˆ— 1 0 βˆ’ 3 )
475720.fig.006e
(e) Three persistent-tumor equilibria with a stable limit cycle ( π‘Ÿ 2 = 0 . 5 and 𝛼 = 1 . 8 βˆ— 1 0 βˆ’ 5 )
475720.fig.006f
(f) Three persistent-tumor equilibria ( π‘Ÿ 2 = 1 and 𝛼 = 4 βˆ— 1 0 βˆ’ 5 )

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