Mathematical and Statistical Methods in Epidemiology

根据英格兰公共卫生部的数据，非常成功的COVID-19疫苗接种计划仅在英格兰就挽救了超过10万人的生命。这一成功的一个贡献因素是疫苗接种计划，老年人和那些有潜在疾病的人首先接种疫苗，正如最近的一些论文所显示的那样。由于疫苗接种计划的明显重要性，本博士项目旨在创建一个数学框架，用于在流行病期间进行疫苗接种的最佳计划。这将利用各种疾病传播的动态模型，以便对可能影响时间表的一些因素进行新的审查，例如家庭规模和以前接触疾病的情况。为了做到这一点，有必要将联合收割机与经典的SIR型房室模型结合起来（其中人口被分成少数群体，允许使用平均数量代替个体感染状态），适用于考虑大人口时，使用更新的网络模型（每个人及其联系人都是单独考虑的），该项目的另一个新方面将是开发一种联合免疫系统，检测和疫苗接种战略，至少对某些人群在接种疫苗前进行检测。当在已经大量暴露于疾病的人群中接种疫苗时，特别是经常导致未发现的无症状感染的人群，这种测试可以帮助显着提高疫苗分配的有效性，特别是如果疫苗供应受到显着限制。为了近似最佳调度，需要开发一种新的算法，因为该问题将具有复杂的，非凸结构此外，大量的人口群体将意味着任何算法都需要非常有效，因为计算任何策略的成功将是耗时的。最终的算法将借鉴文献中的许多现有方法，如贪婪算法（以短期收益为目标）和遗传算法（联合收割机结合好的策略，以试图改善它们）。该算法将被转化为计算机程序，以便进行模拟，以说明其有效性和整体结果。由于一旦该项目完成，COVID-19疫苗接种计划将处于一个非常不同的阶段，主要应用将是为未来流行病的疫苗接种政策提供信息。正因为如此，它将考虑启动疫苗接种计划的若干情景（例如在一波高峰期间或在严格封锁期间）以及关于X疾病和疫苗有效性的一系列不同假设。因此，它将适用于更广泛的-一系列未来的疫苗接种运动，并将帮助那些计划它，以最大限度地提高其有效性。该项目福尔斯数学科学研究领域，如EPSRC网站上所定义。

The highly successful COVID-19 vaccination program has, according to Public Health England, saved over 100 000 lives in the England alone. One contributing factor to this success has been the vaccination schedule, with older people and those with underlying conditions being vaccinated first, as has been shown in a number of recent papers.Motivated by the clear importance of vaccination scheduling, this DPhil project seeks to create a mathematical framework for the optimal scheduling of vaccinations during an epidemic. This will make use of a variety of dynamical models for disease transmission in order to provide a novel examination of a number of factors that could influence the schedule, such as household size and previous exposure to the disease. In order to do this, it will be necessary to combine the classical SIR-type compartmental models (where a population is split into a small number of groups, which allow averaged quantities to be used in place of individual infection statuses), applicable when considering large populations, with more recent network models (where each person and their contacts are considered individually), which will give insight into the dynamics on an individual scale.Another novel aspect of the project will be the development of a combined immunity-testing and vaccination strategy, where at least some groups of people are tested before being vaccinated. When vaccinating in a population that has already had significant exposure to a disease, particularly one that often causes undetected asymptomatic infections, such testing could help to significantly improve the effectiveness of vaccine distribution, particularly if supplies of vaccine are significantly restricted.In order to approximate the optimal scheduling, a novel algorithm will need to be developed, as the problem will have a complicated, non-convex structure. Moreover, the large number of population groups will mean that any algorithm will need to be very efficient, as computation of the success of any strategy will be time-consuming. The final algorithm will draw on many existing approaches in the literature, such as greedy algorithms (which aim for short-term gains), and genetic algorithms (which combine good strategies in order to try to improve them). This algorithm will be turned into a computer program so that simulations can be carried out to illustrate its effectiveness and the overall results.As the COVID-19 vaccination program will be in a very different phase once this project has been completed, the principal application will be to inform vaccination policies for future pandemics. Because of this, it will consider a number of scenarios in which the vaccination program is started (such as during the peak of a wave or during a strict lockdown) alongside a range of different assumptions about a Disease X and the effectiveness of the vaccine.Thus, it will be applicable to a wide-range of future vaccination campaigns and will help those planning it to maximise their effectiveness.This project falls within the mathematical sciences research area, as defined on EPSRC website .