  There is great potential to be explored regarding the use of agent-based
modelling and simulation as an alternative paradigm to investigate early-stage
cancer interactions with the immune system. It does not suffer from some
limitations of ordinary differential equation models, such as the lack of
stochasticity, representation of individual behaviours rather than aggregates
and individual memory. In this paper we investigate the potential contribution
of agent-based modelling and simulation when contrasted with stochastic
versions of ODE models using early-stage cancer examples. We seek answers to
the following questions: (1) Does this new stochastic formulation produce
similar results to the agent-based version? (2) Can these methods be used
interchangeably? (3) Do agent-based models outcomes reveal any benefit when
compared to the Gillespie results? To answer these research questions we
investigate three well-established mathematical models describing interactions
between tumour cells and immune elements. These case studies were
re-conceptualised under an agent-based perspective and also converted to the
Gillespie algorithm formulation. Our interest in this work, therefore, is to
establish a methodological discussion regarding the usability of different
simulation approaches, rather than provide further biological insights into the
investigated case studies. Our results show that it is possible to obtain
equivalent models that implement the same mechanisms; however, the incapacity
of the Gillespie algorithm to retain individual memory of past events affects
the similarity of some results. Furthermore, the emergent behaviour of ABMS
produces extra patters of behaviour in the system, which was not obtained by
the Gillespie algorithm.
