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

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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