Generalised Logistic Differential Equation
A particular case of Richard's function is:
which is the solution of the so called Richard's differential equation (RDE):
with initial condition
where
provided that ν > 0 and α > 0.
The classical logistic differential equation is a particular case of the above equation, with ν =1, whereas the Gompertz curve can be recovered in the limit provided that:
In fact, for small ν it is
The RDE suits to model many growth phenomena, including the growth of tumours. Concerning its applications in oncology, its main biological features are similar to those of Logistic curve model.
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