Our results showed that, apart from the well known differences between these approaches (as those outlined for example, in Schieritz and Milling ), further insight from using ABMS was obtained, such as extra population patterns of behaviour.
These case studies were re-conceptualised under an agent-based perspective and the simulation results were compared with those from the ODE models. In previous work, three case studies using established mathematical models of immune interactions with early-stage cancer were considered in order to investigate the additional contribution of ABMS to ODE models simulation. Furthermore, the emergent behaviour of ABMS produces extra patters of behaviour in the system, which was not obtained by the Gillespie algorithm. 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. 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. These case studies were re-conceptualised under an agent-based perspective and also converted to the Gillespie algorithm formulation. 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. 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. 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. 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.
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