Interactions between heterogeneity and interventions for network epidemics

Abstract

Different sources of heterogeneity in the infection process inherently characterise the transmission mechanisms of many pathogens. SARS-CoV-1 and SARS-CoV-2 were characterised by super-spreading behaviour, where a small number of infections were believed to be responsible for a disproportionate number of transmissions, and changes in the time-varying network of sexual partnerships facilitate the transmission of sexually transmitted infections. In addition to heterogeneity in transmission, the outcomes of infections can be highly heterogeneous; many infections have significant variability in symptoms, often with mild or asymptomatic cases going unnoticed and continuing to infect. Other infections cause mild disease in one sub-population and severe disease in another, such as flu having higher morbidity and mortality rates in older individuals. Naturally, understanding these sources of heterogeneity is vital to the design of effective interventions: vaccines are targeted to the most vulnerable members of society; removing highly connected individuals from a transmission network can prevent many infections; and there exist theoretical results that suggest that contact tracing is highly effective for infections with significant superspreading. However, real-world challenges in implementation, and other sources of heterogeneity in contact tracing, may make it difficult to realise this advantage for infections with superspreading behaviour. As such, in this thesis, our focus is first quantifying the different sources of heterogeneity that can impact the efficacy of epidemic interventions. Then, once we have identified sources of heterogeneity that interventions are sensitive to, we further attempt to quantify the interactions with the design of effective interventions. Given that the SARS-CoV-2 pandemic was ongoing during my PhD studies, it is a natural choice for us to use SARS-CoV-2 as our main focus. The first theme of this thesis focuses on quantifying different sources of heterogeneity that SARS-CoV-2 contact tracing is sensitive to. We develop a household-structured branching process model of contact tracing, which facilitates the modelling of complex contact tracing strategies in structured populations, without the need for fully agent-based simulation. We demonstrate that our assumption of a household-structured population, and long delays in contact tracing, can diminish the advantage of contact tracing in controlling an overdispersed infection process. Additionally, we demonstrate that contact tracing is sensitive to the probability that a symptomatic case reports their symptoms and that interactions between viral load, test sensitivity and infectiousness are potentially very important to understand the efficacy, cost-effectiveness and impact of various strategies. Variations of contact tracing strategies, such as out-of-household isolation and daily contact testing via lateral flow tests, are explored. We also develop a framework for the optimal allocation of limited testing resources in order to maximise contact tracing efficacy. For the second theme of this thesis, motivated by our results that contact tracing efficacy depends on cases self-reporting their symptoms, we develop methods for characterising the co-occurrence patterns of symptoms in community SARS-CoV-2 infections. Gaining insights into the co-occurrence patterns of symptoms allows for better design of symptom-initiated testing and consequently more effective contact tracing. Given that all methodologies for analysing community infections have limitations, we attempt to synthesise results across several datasets. Age is a key source of heterogeneity for SARS-CoV-2, as older cases are subject to significantly higher morbidity levels. We explore whether this leads to symptoms clustering differently across age groups. One key finding is that the clustering of symptoms is most different for the youngest and oldest individuals in our dataset, and symptom-initiated testing criteria should account for this. For the third theme of this thesis, we explore modelling the role of viral load trajectories as a source of significant heterogeneity in epidemics, particularly SARS-CoV-2. Contact tracing is initiated by infected individuals testing positive, and this is more probable in infections with a high viral load, which are also believed to be more infectious. The interaction between viral load and infectiousness is of particular importance when exploring the use of lateral flow tests for infection control, given that they are liable to miss small viral loads, although such individuals may not be highly infectious. However, these interactions between viral load and infectiousness are complicated to quantify using traditional study designs. As such, we develop a methodology that allows us to estimate the relationship between viral load and infectiousness using readily available contact tracing data and imputing key quantities. We use our model to evaluate the efficacy of different infection screening strategies and compare our results to those obtained by simplifying approximations. Overall, we find that significant error can be incurred if the relationship between viral load and infectiousness is not properly modelled when evaluating testing for infection control strategies. This thesis uses approaches from mathematics, statistics, data science and machine learning first to characterise sources of heterogeneity and then explore the impact of the sources of heterogeneity on epidemic interventions. The results we present improve understanding of sources of heterogeneity that are important to consider when designing effective interventions for SARS-CoV-2. In addition, while we have used contact tracing and SARS-CoV-2 as our primary focus, the methodologies and lessons learnt could be readily applied to future epidemics. For example, the chapter on viral load and infectiousness has important consequences for evaluating screening strategies and provides interesting insights into the nature of transmission for respiratory pathogens.

Date of Award	25 Jul 2023
Original language	English
Awarding Institution	The University of Manchester
Supervisor	Lorenzo Pellis (Co Supervisor), Ian Hall (Co Supervisor) & Thomas House (Main Supervisor)