Tumour growth
Mathematical tumour models describe how a tumour population or volume changes through cell proliferation, death and environmental limitation.
Exponential model
\[\frac{dN}{dt}=rN.\]This can approximate early unconstrained growth but cannot represent slowing at larger tumour sizes.
Logistic model
\[\frac{dN}{dt}=rN\left(1-\frac{N}{K}\right).\]Gompertz model
\[\frac{dN}{dt}=rN\ln\left(\frac{K}{N}\right).\]Different growth laws make different assumptions and should be assessed against biological context and data.
Key idea. Tumour growth models provide simplified mathematical descriptions of proliferation and growth limitation rather than universal laws for every tumour.