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，已有超过2.09亿人感染，该病毒导致的全球死亡人数目前已上升至430多万人。这场大流行不仅引发了当局史无前例的政策回应，许多国家进入了长达数月的封锁，而且还引发了国际社会为快速开发疫苗以遏制病毒传播的努力。作为2020年无疑最突出的特征，SARS-CoV-2的出现自然引起了更多不同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，其重点是创建复制人群中传染病行为的模型。除了告知疫情如何演变外，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、部分或全部封锁城市或地区)，并帮助预测每一种情况的结果。然而，尽管出现了多种模型可以解释大流行在全球不同地区的演变，但没有统一的框架，当使用相同的数据进行两种不同的算法时，往往会出现相互冲突的结果。这些模型经常受到描述不佳的方法的影响，而这些研究的发现所基于的软件往往不向普通公众开放。该项目的主要目的是在一个统一的框架内重建和复制目前用于政策制定和新冠肺炎大流行演变预测的各种模型的结果。通过这样做，我们希望比较不同模型的性能，以及开发一个名为epimodels的Python模块。Epimodels被设计为不同流行病学模型的库，使用示例笔记本来显示不同子模块的功能，并配备了所有可用例程的单元测试。这属于EPSRC数学生物学(因为它的重点是流行病学)和软件工程研究领域。这一项目是与罗氏公司合作完成的，其中一个将在“epimodels”模块中展示的模型实际上将是他们自己的模型之一。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。在英国政府列出的用于制定政策的模式中，其他模式也计划在未来增加，例如弗格森模式。该软件将完全开源，并不断得到维护。该Python模块的用户将能够从众多模型中进行选择，其中一个模型与他们试图研究的流行病的特殊性最为相似。它的主要目的是成为流行病学研究的工具，同时也是一种教学资源：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，在其中他们可以工作并添加自己的模型，而且还可以帮助那些对该领域陌生的人了解不同的假设可能如何影响流行病的结果。一些次要目标包括对划分模型选择的时间步长进行定性评估，以及将目前的情况与当局不会采取干预措施的情况进行比较。这项研究将使用的主要数据将集中在英国正在进行的新冠肺炎疫情，以及不同模型选择下的政策如何影响流行病的结果。还将开发推断方法，以评估稳健性并检索相关统计数据，例如复制数量估计。此外，还将使用相同的数据对使用多个模型的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