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Comparing stochastic differential equations and agent-based modelling and simulation for early-stage cancer

Figueredo, Grazziela P.; Siebers, Peer-Olaf; Owen, Markus R.; Reps, Jenna; Aickelin, Uwe

Authors

Grazziela P. Figueredo

Markus R. Owen

Jenna Reps

Uwe Aickelin



Abstract

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.

Journal Article Type Article
Publication Date Jan 1, 2014
Journal PLoS ONE
Electronic ISSN 1932-6203
Publisher Public Library of Science
Peer Reviewed Peer Reviewed
Volume 9
Issue 4
Article Number e95150
APA6 Citation Figueredo, G. P., Siebers, P., Owen, M. R., Reps, J., & Aickelin, U. (2014). Comparing stochastic differential equations and agent-based modelling and simulation for early-stage cancer. PLoS ONE, 9(4), doi:10.1371/journal.pone.0095150
DOI https://doi.org/10.1371/journal.pone.0095150
Keywords Biomedical Informatics, Simulation
Publisher URL http://www.plosone.org/article/info%3Adoi%2F10.1371%2Fjournal.pone.0095150
Copyright Statement Copyright information regarding this work can be found at the following address: http://creativecommons.org/licenses/by/4.0

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://creativecommons.org/licenses/by/4.0





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