Improving inference of pathogen transmissibility and effects of interventions during epidemics.

The context of the research * The threat that infectious diseases pose to plants, animals and humans is one of significant consequence globally [1]. Control of infectious diseases through public health measures is an intensely researched area (due to their effectiveness [2]), particularly during the early stage of an epidemic. Since the turn of the century, continual tracking of the time-dependent reproduction number, R_t, has increasingly become more helpful to guide how interventions should change through time. R_t is defined as the expected number of secondary cases generated by an infectious case once an epidemic is underway [3]. This statistic indicates the magnitude of the intervention required to control the outbreak (e.g. the proportion of contacts that must be prevented for cases numbers to begin falling), for the given pathogen. Given perfect contact tracing information, inferring the time dependent reproductive number (at time t) would be as simple as counting the average number of secondary cases that a primary case generates at time t. It is important to note that we require real-time estimates to inform decision making but the 'perfect information' approach described here can only be generated retrospectively. In reality, such information is not available and instead, R_t inference is estimated using two types of data. One data type is incidence (number of new symptomatic cases), whilst the other concerns an epidemiological delay distribution between all infector-infectee pairs. The second piece of data would ideally be the generation interval (the distribution of delays from infection in a primary case to infection in a secondary case) and in which case the incidence data would be indexed to the date of infection. In practice, a proxy for the generation interval is used (owing to the complexity and ambiguity of determining exactly when an infectee becomes infected). This is the so-called the 'serial interval' (the distribution of delays between symptom onset in an infectorinfectee pair). To infer the time-dependent reproduction number accurately, one should then index the incidence data with date of symptom onset. Broadly speaking, there are two statistical methods ([5] and [6]) which a large number of studies base their R_t inferences on. Both of these methods use Bayesian inference techniques to generate time-evolving confidence intervals and expectations for R_t. This project will involve building on the work developed in [5]. Accurate and precise R_t estimation is of significance during an epidemic since it is the primary indicator of the necessary stringency of public health measures. Consequently, the lack of accurate or precise estimates can lead to either delays in bringing outbreaks under control (resulting in excess morbidity and mortality) in the event that R_t is under-estimated or conversely, unnecessary public health measures in the vent that R_t is over-estimated. Currently none of these estimates include non-static (time evolving) serial interval (the distribution of delays between symptom onset in an infectorinfectee pair) estimates. There is preliminary evidence ([9], [11]) to suggest that time evolving serial intervals may have a significant impact on R_t estimates. Aims: To improve the techniques that generate R_t estimates and to develop the understanding (within the field of mathematical epidemiology) about the significance (if any) of time varying serial intervals on R_t inference. Objectives: Develop a hypothesis on how characteristics of changing serial intervals will affect R_t inference. Investigate real world data (initially from the 2018-2020 Ebola epidemic in Beni Health Zone, North Kivu Province, DRC), where I can infer the reproductive number (with and without updating serial intervals) to test my hypothesis. Extend existing theory on R_t inference to incorporate heterogeneities into the model framework, e.g. spatial/age models External Partners - WHO