the dynamics of waning and boosting of immunity: new modelling and numerical tools

Population immunity as a public health concern. The decay of immunity to an infectious pathogen can cause the replenishment of the pool of susceptible individuals and hence recurring epidemic outbreaks in the population. Think, for instance, at the recent outbreaks caused by the Omicron SARS-CoV-2 variant or measles. Additionally, understanding boosting of immunity through re-exposure to the pathogen is key when designing vaccination programmes, especially when the vaccine protection is imperfect or temporary, as in the case of chickenpox and shingles. Understanding the consequences of waning and boosting of immunity - acquired either through infection or vaccination - on the population-level epidemic is therefore fundamental for public health planning and, in this sense, this project aligns with the United Nations' Sustainable Development Goal 3 ("Good Health and Well-Being") and the UKRI strategic themes "Building a secure and resilient world", "Securing better health, ageing and wellbeing" and "Tackling Infections". Mathematical models of waning and boosting of immunity. Immunity waning and boosting are particularly challenging to describe mathematically as their effects can be delayed, and overly simplified models can disregard interesting model outcomes like periodic oscillations. Models structured by the time passed since infection or recovery, formulated as integral or partial differential equations, are the most appropriate as they allow a flexible definition of the within-host dynamics informed by the underlying physiology, which are then related to the between-host infection rates. However, these models were under-exploited during the COVID-19 pandemic mostly due to their theoretical and numerical complexity and the lack of accessible software tools. This project combines state-of-the art theoretical and numerical methods to investigate the dynamics of structured models with waning and boosting of immunity when varying model parameters. The project aims to: O1. Develop new mathematical models for waning immunity that balance simplicity and flexibility; O2. Investigate the impact that different assumptions on the within-host parameters have on the population dynamics outcomes of the model; O3. Investigate complex dynamical behaviour -including the emergence of bistability and chaos- caused by waning and boosting of immunity; O4. Develop mathematical tools to predict the growth rate of an emerging variant of concern. Impact and timeliness. The team brings together modelling and numerical expertise on structured models and a strong experience in public health and policy advice. Theoretical and numerical results to study the dynamics of structured models have been rigorously developed only in the last decade, and this is the best time to combine those to generate new understanding. This project will provide evidence and understanding to modellers on how time-since-infection models and detailed within-host dynamics are essential to characterise and explore the population-level disease trends in the presence of waning and boosting of immunity. The models will be used to provide a pragmatic tool for intervention planning in response to the invasion of new, potentially immunoevasive, pathogen variants. This project is one of the first steps of a larger research programme by the co-leads aiming at highlighting the importance of time-since-infection models and, most importantly, creating easy-to-use tools to make them accessible in the future. Preparation to major national risks, such as a pandemic, is best conducted outside emergencies, and we are now in the best position to combine mathematical methods developed in the last decade with the expertise and large amount of data coming from the vivid experience of COVID-19.