System Dynamics from Individual Interactions: A process algebra approach to epidemiology

疾病可以被视为一种威胁或一种工具。现代社会已经变得容易受到广泛传播的流行病的影响，但我们也使用疾病来控制农作物中的害虫，以此作为避免使用化学品的一种方式。显然，能够理解疫情的运作方式是很重要的：有多少人口将被感染？个人的行为是否改变了疾病的传播？这种疾病需要多长时间才能消失？控制疾病的最有效方法是什么？实验测试不是一种选择：让人们感染疾病只是为了看看会发生什么，这存在伦理问题，因此我们使用数学模型。这些帮助我们预测流行病的形态并评估控制方法。在这个项目中，被称为进程代数的理论计算机科学技术将被用来为疾病建模。这种方法的独特好处有三个方面。首先，直接描述个人的行为是可能的。其次，这些个体可以被严格地组合在一起，给出整个系统的行为。第三，可以对系统进行正式调查，以确定系统动力学的特征，从而使我们能够回答上面提出的问题。这种以个人为基础的方法特别重要，因为在现实中，我们可以衡量关于个人的事实，但我们关于流行病的问题都来自人口层面。在描述疾病传播时，能够严格地在不同的抽象水平(个人到人群)之间移动，这给了我们全新的流行病学思维方式。我们的团队在这项工作中处于世界领先地位，但我们正处于长期研究计划的开始。在以前的工作中建立了描述和研究简单疾病系统的领域专业知识和技术和工具后，我们现在可以考虑更复杂的流行病学现象，这些现象所需的特殊建模特征，以及进一步的研究方法。在这个项目中，我们将建立和研究与流行病学相关的特定生物特征的过程代数模型。它们是：波动的人口(增加出生和死亡)，互动和传播(如果我对你打喷嚏，你会感染我的流感吗？房间里的其他人呢？)、控制(有多少人口需要接种疫苗才能保护整个人口免受疾病侵袭？)，以及个体之间的竞争(如果我没有足够的食物，会不会使我更容易感染疾病？)。这些特征已被选为代表人口和流行病学模型的核心，它们一起提供了一个更现实和更全面的疾病模型。探索更复杂的生物系统将需要更复杂的模型。进程代数具有足够的表现力来描述这些系统；然而，这样的描述可能会笨拙且难以理解。我们将开发新的语言结构，使人口模型能够更简单地表达，产生更容易构建和理解的模型。一旦模型被构建，我们就有了一系列正式的技术来研究它的行为，并与文献中其他现有的模型进行比较。我们将根据流行病学系统的需要，进一步发展这些调查技术。最后，尽管我们将重点放在流行病学上，但所开发的特征和技术将适用于生物学的其他领域，以及计算机科学。例如，我们可以将个体视为单个细胞或复杂分子，而不是将其视为人或动物。在计算机科学领域，我们可以使用流行病模型来考虑性能建模，也可以使用恶意软件(计算机病毒、蠕虫等)。这种普遍适用性使我们的工作特别令人兴奋。

Disease can be viewed as a threat or as a tool. Modern society has become vulnerable to wide spreading epidemics, but we also use diseases to control pests in crops as a way of avoiding the use of chemicals. Clearly it is important to be able to understand the way the epidemic works: How much of the population will be infected? Does the behaviour of individuals change the spread of the disease? How long will it take before the disease dies out? What is the most effective way to control the disease?Testing experimentally is not an option: there are ethical problems with infecting people with diseases just to see what happens, therefore we use mathematical models. These help us predict the shape of epidemics and to evaluate methods of control. In this project theoretical computer science techniques known as process algebras will be used to model diseases. The unique benefits of this approach are threefold. Firstly, it is possible to describe the behaviour of individuals directly. Secondly, those individuals can be rigorously combined to give the behaviour of the system as a whole. Thirdly, the system can be formally investigated to establish features of the system dynamics, allowing us to answer the sort of questions posed above. This approach, known as individual-based, is particularly important because in reality we can measure facts about individuals, but our questions about epidemics all come from the population level. The ability to move rigorously between different levels of abstraction (individual to population) when describing disease spread gives us completely new ways of thinking about epidemiology.Our group is the foremost in the world in this work, but we are at the start of a long term research programme. Having built up domain expertise and techniques and tools for describing and investigating simple disease systems in previous work, we are now in a position to consider more complex epidemiological phenomena, the particular modelling features required for these, and further methods of investigation.In this project we will build and investigate process algebra models of specific biological features associated with epidemiology. These are: fluctuating populations (Adding births and deaths), interaction and transmission (If I sneeze on you, will you get my flu? What about the others in the room?), control (How many of the population need to be vaccinated to protect the whole population from the disease?), and contest between individuals (If I don't have enough food will that make me more susceptible to disease?). These features have been chosen as core to the representation of population and epidemiological models and together give a more realistic and rounded model of disease.Exploration of more complex biological systems will require more complex models. Process algebra is expressive enough to describe these systems; however, such descriptions may be clumsy and hard to understand. We will develop new language constructs to allow population models to be more simply expressed, yielding more easily constructed and understood models. Once the model is constructed we have a range of formal techniques to investigate its behaviour, and to compare with other existing models in the literature. We will develop those investigative techniques further, based on the needs of epidemiological systems.Finally, although we will concentrate on epidemiology, the features and techniques developed will be applicable to other areas of biology, and to computer science. For example, instead of viewing an individual as a person or an animal, we could view an individual as a single cell or a complex molecule. In the computer science arena, we can use epidemiological models to think about performance modelling, and also malware (computer viruses, worms etc). This general applicability makes our work particularly exciting.