  We propose an extension of a standard stochastic individual-based model in
population dynamics which broadens the range of biological applications. Our
primary motivation is modelling of immunotherapy of malignant tumours. In this
context the different actors, T-cells, cytokines or cancer cells, are modelled
as single particles (individuals) in the stochastic system. The main expansions
of the model are distinguishing cancer cells by phenotype and genotype,
including environment-dependent phenotypic plasticity that does not affect the
genotype, taking into account the effects of therapy and introducing a
competition term which lowers the reproduction rate of an individual in
addition to the usual term that increases its death rate. We illustrate the new
setup by using it to model various phenomena arising in immunotherapy. Our aim
is twofold: on the one hand, we show that the interplay of genetic mutations
and phenotypic switches on different timescales as well as the occurrence of
metastability phenomena raise new mathematical challenges. On the other hand,
we argue why understanding purely stochastic events (which cannot be obtained
with deterministic models) may help to understand the resistance of tumours to
therapeutic approaches and may have non-trivial consequences on tumour
treatment protocols. This is supported through numerical simulations.
