The mathematical modelling of metastasis is a challenge. The occurrence of metastasis is basically random, hence the use of stochastic modelling seems appropriate. We introduce a stochastic process called branched random walk with settlement to derive equations for the expected number of particles, the variance, the furthest particle and the extinction probability. We are able to identify a parameter $R_0$, such that metastasis spread for $R_0>1$ and they die out for $R_0<1$. Hence we call $R_0$ the metastatic reproduction number. We compare this index to experimental outcomes in animal studies and we discuss its relevance for the treatment of metastasis.
Joint work with A. Rhodes and C. Frei.