  We give a very short introduction to discrete and continuum models for the
evolutionary and spatial dynamics of cancer through two case studies: a model
for the evolutionary dynamics of cancer cells under cytotoxic therapy and a
model for the mechanical interaction between healthy and cancer cells during
tumour growth. First we develop the discrete models, whereby the dynamics of
single cells are described through a set of rules that result in branching
random walks. Then we present the corresponding continuum models, which are
formulated in terms of non-local and nonlinear partial differential equations,
and we summarise the key properties of their solutions. Finally, we carry out
numerical simulations of the discrete models and we construct numerical
solutions of the corresponding continuum models. The biological implications of
the results obtained are briefly discussed.
