早期癌症的随机微分方程和基于Agent的建模与仿真比较
Comparing Stochastic Differential Equations and Agent-Based Modelling and Simulation for Early-stage Cancer
摘要：
关于使用基于代理的建模和模拟作为另一种范式来研究早期癌症与免疫系统的相互作用，有很大的潜力有待探索。它不受常微分方程模型的一些限制，如缺乏随机性，代表个人行为而不是总量和个人记忆。在本文中，我们调查的潜在贡献基于代理的建模和模拟时，与随机版本的ODE模型，使用早期癌症的例子。我们寻求以下问题的答案：（1）这种新的随机制定产生类似的结果，以代理为基础的版本？(2)这些方法可以互换使用吗？(3)与Gillespie的结果相比，基于代理人的模型结果是否显示出任何好处？为了回答这些研究问题，我们研究了三个完善的数学模型，描述肿瘤细胞和免疫元素之间的相互作用。这些案例研究重新概念化的代理人为基础的角度来看，也转换为Gillespie算法制定。因此，我们对这项工作的兴趣是建立一个关于不同模拟方法可用性的方法论讨论，而不是提供进一步的生物学见解调查的案例研究。我们的研究结果表明，它是可能的，以获得等价的模型，实现相同的机制，然而，Gillespie算法的无能，以保留个人的记忆，过去的事件影响了一些结果的相似性。此外，ABMS的涌现行为在系统中产生了额外的行为模式，这是吉莱斯皮算法无法获得的。
英文摘要：
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.
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