Mathematical and Statistical Methods in Epidemiology

据英国公共卫生部称，仅在英格兰，非常成功的COVID-19疫苗接种计划就挽救了10多万人的生命。这一成功的一个促成因素是疫苗接种计划，正如最近一些论文所显示的那样，老年人和那些有潜在疾病的人首先接种疫苗。由于疫苗接种计划的明确重要性，该博士项目旨在为流行病期间疫苗接种的最佳计划创建一个数学框架。这将利用疾病传播的各种动态模型，以便对可能影响时间表的一些因素，如家庭规模和以前接触疾病的情况，进行新的检查。为了做到这一点，有必要将经典的sir型隔间模型（将人群分成少数群体，允许使用平均数量代替个体感染状态）与最近的网络模型（将每个人及其接触者单独考虑）结合起来，这将有助于深入了解个体尺度上的动态。该项目的另一个新颖方面将是开发一种免疫检测和疫苗接种相结合的策略，在接种疫苗之前至少对某些人群进行检测。当在已经大量接触某种疾病的人群中接种疫苗时，特别是在经常引起未被发现的无症状感染的人群中，这种测试可以帮助显著提高疫苗分发的有效性，特别是在疫苗供应严重受限的情况下。为了逼近最优调度，需要开发一种新的算法，因为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高效，因为计算任何策略的成功都将花费大量时间。最后的算法将借鉴文献中许多现有的方法，如贪心算法（以短期收益为目标）和遗传算法（结合良好的策略以试图改进它们）。该算法将被转换成计算机程序，以便进行模拟以说明其有效性和总体结果。一旦该项目完成，COVID-19疫苗接种规划将进入一个非常不同的阶段，因此主要应用将是为未来大流行的疫苗接种政策提供信息。因此，它将考虑启动疫苗接种计划的多种情况（例如在流感高峰期或严格封锁期间），以及关于X疾病和疫苗有效性的一系列不同假设。因此，它将适用于未来广泛的疫苗接种运动，并将帮助那些计划接种运动的人最大限度地发挥其效力。根据EPSRC网站的定义，该项目属于数学科学研究领域。

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 .