From: Differences in predictions of ODE models of tumor growth: a cautionary example
Model | Maximum | Doubling | Growth |
---|---|---|---|
size | time | condition | |
Exponential | ∞ | \(\frac {\ln 2}{a}\) | a>0 |
Mendelsohn | ∞ | \(\frac {\ln 2}{a}\) | a>0 |
Logistic | b | \(\frac {\ln 2}{a}\) | a>0 |
Linear | ∞ | \(\frac {b\ln 2}{a}\) | \(\frac {a}{b}>0\) |
Surface | ∞ | \(\frac {b^{\frac {1}{3}}\ln 2}{a}\) | \(\frac {a}{b^{\frac {1}{3}}}>0\) |
Gompertz | b−c | \(\frac {\ln 2}{a\ln \left (\frac {b}{c}\right)}\) | \(a\ln \left ({\frac {b}{c}}\right)>0\) |
Bertalanffy | \(\left (\frac {a}{b}\right)^{3}\) | \({\frac {\ln 2}{a-b}}\) | a−b>0 |