# 2018 Annual Meeting of the Society for Mathematical Biology & the Japanese Society for Mathematical Biology

8-12 July 2018
Australia/Sydney timezone

## The metastatic reproduction number

12 Jul 2018, 11:30
30m
New Law School/--024 (University of Sydney)

### New Law School/--024

#### University of Sydney

100
Oral Presentation Minisymposium: Mathematical models of cell motility and cancer progression in microenvironment

### Speaker

Prof. Thomas Hillen (University of Alberta)

### Description

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.

### Primary author

Prof. Thomas Hillen (University of Alberta)

### Presentation Materials

There are no materials yet.