Simulating COVID-19 cases and deaths using compartmental differential equation models

自2019年底在中国武汉地区发现新型冠状病毒SARS-Cov-2以来，全球已有超过2.09亿人感染，该病毒造成的死亡人数现已上升至430多万人。这次大流行不仅引发了当局前所未有的政策反应，许多国家进入了长达数月的封锁状态，而且还引发了国际上快速开发疫苗以遏制病毒传播的努力。毫无疑问，作为2020年最突出的特征，SARS-Cov-2的出现自然引起了更多样化受众对流行病学研究的兴趣增加。流行病学建模是数学生物学的一个分支，其重点是创建复制传染病在人群中的行为的模型。除了为疫情演变提供信息外，这些模型还可用于指导政府机构的公共卫生干预措施（例如疫苗接种运动、部分或全面封锁城市或地区），并帮助预测每种情况的结果。然而，尽管出现了多种模型，可以解释全球不同地区大流行的演变，但没有统一的框架，在对两种不同的算法使用相同的数据时，往往会出现相互矛盾的结果。这些模型经常受到方法论描述不佳的影响，而这些研究结果所基于的软件通常不向公众开放。该项目的主要目的是在统一的框架内重建和重现目前用于政策制定和预测Covid-19大流行演变的各种模型的结果。通过这样做，我们希望比较不同模型的性能，并开发一个Python模块“epimodels”。Epimodels被设计为不同流行病学模型的库，带有示例笔记本以显示不同子模块的功能，并为所有可用例程配备了单元测试。这属于EPSRC数学生物学（因为它关注流行病学）和软件工程研究领域。这个项目是与罗氏合作完成的，其中一个模型将在“epimodels”模块中展出，实际上是他们自己的一个。目前，该图书馆包含一个模型，由英国公共卫生（PHE）使用，并与剑桥大学共同开发。其他被英国政府列为政策制定中使用的模型，如弗格森模型，计划在未来加入。该软件将是完全开源的，并将持续维护。这个Python模块的用户将能够从众多模型中选择一个最接近他们正在研究的流行病的特征的模型。它的主要目的是成为流行病学研究的一种工具，同时作为一种教学资源：它不仅可以帮助那些在流行病学研究方面更有经验的人找到一个现成的框架，他们可以在其中工作并可以添加自己的模型，而且还可以帮助那些新进入该领域的人了解不同的假设如何影响流行病的结果。一些次要目标包括对分区模式所选择的时间步骤进行定性评估，以及将目前的情况与当局不采取干预措施的情况进行比较。本研究将使用的主要数据将集中在英国正在进行的Covid-19流行病以及政策如何影响不同模型选择的流行病结果。还将开发推断方法来评估稳健性和检索相关统计数据，例如再现数估计。此外，将使用使用相同数据的多个模型对流行病概况进行比较分析，以评估哪些模型最适合特定的模拟制度和不同类型的数据

Since the discovery of the new coronavirus SARS-Cov-2 in the region of Wuhan, China in late 2019, more than 209 million people have been infected and the number of deaths caused by this virus has now risen to over 4.3 million worldwide. This pandemic has not only triggered policy responses of unprecedented scale from authorities, with many countries going into months-long lockdown, but also international efforts for the fast development of vaccines to temper the virus' spread. As the undoubtedly most prominent feature of the year 2020, the emergence of SARS-Cov-2 has naturally caused an increase in interest in epidemiological research from a more diverse audience. Epidemiological modelling is a branch of mathematical biology that focuses on creating models that replicate the behaviour of infectious diseases in a population. Apart from informing how the epidemic evolves, these models can be used to direct public health interventions by government bodies (e.g. vaccination campaigns, partial or full lockdown of cities or regions) and help predict the outcome for each such scenario. However, despite the emergence of multiple models that could explain the evolution of the pandemic in different regions of the globe, no unified framework exists, and conflicting results often arise when using the same data for two distinct algorithms. These models often suffer from poorly described methodology and the software on which those studies base their finding are very often not open to the general public. The principal aim of this project is to reconstruct and reproduce the results of various models currently used in policy making and the prediction of the evolution of the Covid-19 pandemic, in a unified framework. By doing so, we hope to compare the performance of different models, as well as develop a Python module 'epimodels'. Epimodels is designed as a library of different epidemiological models, with example notebooks to show the functionalities of the different submodules and is equipped with unit tests for all usable routines. This falls within the EPSRC Mathematical Biology (for its focus on epidemiology), and Software Engineering research areas. This project is done in partnership with Roche and one of the models to be featured in the 'epimodels' module will be in fact one of their own. Currently, the library contains one model, used by Public Health England (PHE) and developed with the University of Cambridge. Other models among those listed by the UK government as being used in policy making, e.g. the Ferguson model are planned to be added in the future. The software will be entirely open-source and constantly maintained. Users of this Python module will be able to choose from a multitude of models one that resembles the most the particularities of the epidemic they are trying to study. Its main purpose is to become a tool for epidemiological research with the added benefit of being a pedagogical resource at the same time: it can help not only those more experienced with epidemiological research find a ready-made framework in which they can work and can add their own model but also those new to the field understand how different assumptions may impact the outcome of an epidemic. Some secondary objectives include a qualitative assessment of the time-step chosen for compartmental models, as well as a comparison of the current situation with the scenario when no interventions would have been taken by the authorities. The main data that will be used for this research will focus on the ongoing Covid-19 epidemic in England and how policies impact the outcome of the epidemics for different choices of models. Inference methods will also be developed to assess robustness and retrieve relevant statistics, e.g. reproduction number estimates. Also, a comparative analysis of the epidemic profile using multiple models using the same data will be done to assess which models are best for specific simulation regimes and different types of da