Abstract
Many advances in research regarding immuno-interactions with cancer were developed with the help of ordinary differential equation (ODE) models. These models, however, are not effectively capable of representing problems involving individual localisation, memory and emerging properties, which are common characteristics of cells and molecules of the immune system. Agent-based modelling and simulation is an alternative paradigm to ODE models that overcomes these limitations. In this paper we investigate the potential contribution of agent-based modelling and simulation when compared to ODE modelling and simulation. We seek answers to the following questions: Is it possible to obtain an equivalent agent-based model from the ODE formulation? Do the outcomes differ? Are there any benefits of using one method compared to the other? To answer these questions, we have considered three case studies using established mathematical models of immune interactions with early-stage cancer. These case studies were re-conceptualised under an agent-based perspective and the simulation results were then compared with those from the ODE models. Our results show that it is possible to obtain equivalent agent-based models (i.e. implementing the same mechanisms); the simulation output of both types of models however might differ depending on the attributes of the system to be modelled. In some cases, additional insight from using agent-based modelling was obtained. Overall, we can confirm that agent-based modelling is a useful addition to the tool set of immunologists, as it has extra features that allow for simulations with characteristics that are closer to the biological phenomena.
Highlights
Advances in cancer immunology have been facilitated by the joint work of immunologists and mathematicians [1,2,3]
The number of effector cells for both simulations follow the same pattern, the numbers are not the same due to the agents variability. This variability is very evident with regards to the effector cells population for two main reasons: (1) for this first case study the size of the populations involved is relatively small, which increases the impacts of stochasticity in the outcomes; and (2) the ordinary differential equation (ODE) system changes the amount of cells overtime in a continuous fashion, which means that in this simulation fractions of cells are considered
The ABMS was validated by comparing its outputs with those produced by the ODEs
Summary
Advances in cancer immunology have been facilitated by the joint work of immunologists and mathematicians [1,2,3]. Most existing mathematical models in cancer immunology are based on sets of ordinary differential equations (ODEs) [2]. This approach, has limitations pertaining problems involving spatial interactions or emerging properties [4,5]. An alternative to ODE modelling that overcomes these limitations is systems simulation modelling. It is a set of methodologies and applications which mimic the behaviour of a real system [6,7,8]. In a simulation environment it is possible to systematically generate different scenarios and conduct experiments. The “what-if” scenarios studied in such an environment do not require ethics approval
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