Cancer-growth project
A simple tumour model can begin with logistic growth:
\[\frac{dV}{dt}=rV\left(1-\frac VK\right),\]where \(V(t)\) is tumour volume, \(r\) a growth-rate parameter and \(K\) an effective carrying capacity.
Treatment extension
A simplified treatment effect can be represented by an additional loss term:
\[\frac{dV}{dt}=rV\left(1-\frac VK\right)-u(t)V,\]where \(u(t)\) describes an assumed time-dependent treatment effect.
Investigation
Compare untreated and treatment scenarios and explore sensitivity to \(r\), \(K\) and the assumed treatment schedule. Interpret results only within the biological assumptions of the simplified model.
Project outcome. Learn how growth and treatment mechanisms can be represented as competing terms in a dynamical model.