My PhD student Chay Paterson, Martin Nowak (Harvard) and I have just published a paper about a (relatively) simple mathematical model of cancer. The article in Scientific Reports shows (among others) how migration of cancer cells from the primary lesion can lead to a faster growth of the tumour.

We have seen this already in this paper, but Chay’s paper shows mathematically how this is possible. For example, we show that if a single, “ball-like” lesion expands at rate *v* cells/day, and cells migrate from the surface and establish new lesions with probability *M*, then the whole tumour grows exponentially with rate

This is true (modulo a small correction) even if individual lesions grow slower with time.

The model is exactly solvable, although some formulas are rather lengthy. Here is a small sample: