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Many advances in research regarding immuno-interactions with cancer weredeveloped with the help of ordinary differential equation (ODE) models. Thesemodels, however, are not effectively capable of representing problems involvingindividual localisation, memory and emerging properties, which are commoncharacteristics of cells and molecules of the immune system. Agent-basedmodelling and simulation is an alternative paradigm to ODE models thatovercomes these limitations. In this paper we investigate the potentialcontribution of agent-based modelling and simulation when compared to ODEmodelling and simulation. We seek answers to the following questions: Is itpossible to obtain an equivalent agent-based model from the ODE formulation? Dothe outcomes differ? Are there any benefits of using one method compared to theother? To answer these questions, we have considered three case studies usingestablished mathematical models of immune interactions with early-stage cancer.These case studies were re-conceptualised under an agent-based perspective andthe simulation results were then compared with those from the ODE models. Ourresults show that it is possible to obtain equivalent agent-based models (i.e.implementing the same mechanisms); the simulation output of both types ofmodels however might differ depending on the attributes of the system to bemodelled. In some cases, additional insight from using agent-based modellingwas obtained. Overall, we can confirm that agent-based modelling is a usefuladdition to the tool set of immunologists, as it has extra features that allowfor simulations with characteristics that are closer to the biologicalphenomena.

Investigating Mathematical Models of Immuno-Interactions with Early-Stage Cancer under an Agent-Based Modelling Perspective