A major hazard to public health is the resurgence of infectious diseases that were once believed to be eliminated from a population [1]. Recent examples include regional resurgences of Polio after an exhaustive vaccination campaign [2], the rise of syphilis after decades of antibiotics had largely made it a disease of the past [3], and an uptick of tuberculosis following the onset of war [4]. While each case tells its own unique story, they each raise the same important question: at what point can we declare that a disease is eliminated, and how do we ensure long-term security after this has been achieved?

Mathematical modelling is useful to contextualise various stages of an epidemic. While pathogen emergence, exponential epidemic growth, endemicity, and the effects of interventions have all been modelled extensively [5], the post-elimination risk of disease resurgence has not. There is no established framework we can apply to assess the risk of disease reemergence in an environment once hostile to the pathogen.

The World Health Organisation has ambitious targets for disease elimination, for example viral Hepatitis by 2030 [6], but less has been said about how disease security is maintained in the following years.

Aims & Objectives: This project aims to advance the field of mathematical epidemiology in the area of infectious disease resurgence, and provide insights to help maintain health security following the elimination of an infectious disease.

Objectives:
(O1) Formulate a robust definition of disease elimination based on the risk of resurgence
(O2) Build a taxonomy of resurgent diseases and reasons behind cases of resurgence
(O3) Define mathematically the conditions that lead to resurgence following a successful elimination campaign
(O4) Develop modelling tools to inform policy decisions regarding resurgence
(O5) Study cases of potential resurgence in real-world settings such as viral hepatitis after 2030

Methods are categorised as follows:
Literature review: For O1 and O2, the candidate will develop skills in performing narrative and, possibly, systematic literature reviews. They will obtain deep knowledge of epidemiology and public health responses to infectious disease threats.

Mathematical modelling: For O3 (and potentially O4) the candidate will become proficient in formulating a mathematical model, then applying analytical and numerical techniques to extract insights about the system. They will develop expertise in random variables and a deep understanding of rare extreme events.

Computational modelling: For O4, simulation models will be coded in python, R, or Matlab. They will develop bespoke models for specific disease systems from existing resources, e.g. the Gillespe algorithm for stochastic processes, agent-based modelling for encoding complex behavioural characteristics.

Incorporating data: For O5, the candidate will apply data handling, visualisation, and statistical analysis to epidemiological and behavioural data. Advanced methods (e.g. Bayesian) will be applied to calibrate models to particular disease settings. Where necessary, high performance computing facilities will be utilised.

Communication: The candidate will develop skills in communicating scientific results to relevant stakeholders. This may include engagement with policy, the public, and other academics.

Training Plan: The candidate will initially be assessed to identify areas of interest and skills to be developed. They will be integrated into our wider research group and immediately benefit from the support of a diverse group of researchers with expertise in quantitative methodologies, evidence synthesis, epidemiology and modelling. They will join a peer group of 11 other PhD students within our team who meet biweekly. In addition to relevant courses within the university, they will be encouraged to attend summer schools, conferences, and participate in a work placement within UKHSA which we will help to arrange.

References:
[1] Re-emergence of infectious diseases associated with the past, Venkatesan, Lancet Microbe, 2021
[2] Wild poliovirus makes comeback in Afghanistan and Pakistan, Roberts, Science, 2024
[3] The resurgence of syphilis in high-income countries in the 2000s: a focus on Europe, Spiteri et al. Epidemiology and Infection, 2019
[4] Tuberculosis in times of war and crisis: Epidemiological trends and characteristics of patients born in Ukraine, Germany, 2022, Hauer et al. Eurosurveillance, 2023
[5] Modeling infectious diseases in Humans and animals, Keeling and Rohani, 2008
[6] Guidance for country validation of viral hepatitis elimination and path to elimination, World Health Organisation, 2023