Translating simulation approaches for immunology

This thesis presents a novel set of guidelines to convert between simulation modelling approaches, namely, Ordinary differential Equations (ODEs), System Dynamics (SD) and Agent-based Modelling and Simulation (ABMS). In our literature review we identify a gap in establishing translation techniques between these approaches. We therefore focus our research in developing these techniques and assessing the impact of these conversions in the simulation outcomes. In particular, our interest lies in investigating our techniques applied to simulation problems for the immune system, as we wish to aid immunologists with the choice of the most appropriate approach for a certain problem. The aims of this thesis are therefore defined as: (1) with no explicit guidelines available from the literature, we want to develop, test and validate our own set of guidelines for converting between approaches: from ODE models to SD, from SD to ABMS and from ABMS to SD; and (2) we seek to discuss the merits of SD and ABMS for Immunology to assist researchers with the choice between both approaches. The assessment of the effectiveness of the conversion guidelines is achieved by using a case study approach involving six cases of established mathematical models describing immunological phenomena. These case studies are chosen by considering aspects such as the behaviour of the entities of the model (whether they are static or interact with other entities and whether they have spatial representation or not), the type of hypothesis to be tested, the empirical embeddedness of real data, population sizes, number of elements involved and the modelling effort. In order to conduct our conversion for the case studies, we first convert their original ODE model into an SD model, and then perform the translation from SD to ABMS. For the last three case studies, we also test the conversion guidelines from ABMS to SD. Evidence from the experiments reveal that for all cases it was possible to obtain equivalent approaches by using the conversion guidelines developed. However, outcome differences occur given the intrinsic characteristics of each simulation modelling paradigm. By observing these differences we could conclude that (1) SD is incapable of reflecting exactly the same variability as that obtained from the agent-based simulation, as it is a deterministic approach; (2) SD variables change continuously in time and therefore population numbers over time might be different from those obtained by the agent-based simulation; (3) as the number of different agents and behaviours increase, the corresponding SD becomes very intricate and difficult to develop and understand; (4) there are cases where it is preferable not to convert from ABMS to SD, as the agent-based model is easier to conceptualise and implement; (5) For other circumstances, ABMS outcomes are the same as those produced by the ODEs and SD, with the disadvantage to be more resource consuming in terms of computational memory and processing capacity; and (6) For some cases SD is less informative than ABMS, as it does not produce multiple scenarios or variations over the course of more than one run within the same parameters