Theory and Modern Applications
Table 1 Description of the parameters according to the literature [14]
From: Neimark–Sacker bifurcation of a chemotherapy treatment of glioblastoma multiform (GBM)
Parameter | Rate | |
|---|---|---|
p | Division rate of SC | 0.192 |
\(K_{1}\) | Carrying capacity of GC concentration | 510 kg/m3 |
\(K_{2}\) | Carrying capacity of NC and SC together | 340 kg/m3 |
\(K_{3}\) | Carrying capacity of RC | 170 kg/m3 |
ρ | The mutation rate of SC to RC | ρ∈[10−5,10−2] |
\(\alpha _{i}\), \(\beta _{i}\) | The logistic population rate of GC and SC, respectively | \(\alpha _{i},\beta _{i} \in [ 0.2, 0.95 ]\) |
\(\gamma _{i}\) | The logistic population rate of RC | \(\gamma _{i} \in [ 0.05, 0.2 ]\) |
\(r_{1}\) | The growth rate of GC | 0.0068 |
\(r_{2}\) | The growth rate of SC | 0.012 |
\(r_{3} \) | The growth rate of RC | \(r_{3} = ( 1.05 ) * r_{2}\) |
\(\mu _{i}\) | Competition between GC and CC, \(\mu _{1} = \mu _{3} =3.6\times 10^{-5}\), \(\mu _{2} =3.6\times 10^{-6}\) and \(\mu _{4} =3.6\times 10^{-7}\) | [3.6 × 10−7,3.6 × 10−5] |
\(P_{1}\) | Predation coefficient of GC | 2.4 × 10−5 |
\(P_{2}\) | Prediction coefficient of SC | 2.4 × 10−2 |
\(P_{3}\) | Prediction coefficient of RC | 2.4 × 10−2 |
σ | Chemotherapy agent rate for infusion | 0–150 |
\({\omega }_{{i}}\) | Chemotherapy agent rate for washout | 0.2 |