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

In the 2018 Government Office for Science report, 'Computational Modelling: Technological Futures', Greg Clarke, the Secretary of State for Business Energy and Industrial Strategy, wrote "Computational modelling is essential to our future productivity and competitiveness, for businesses of all sizes and across all sectors of the economy". With its focus on computational models, the mathematics that underpin them, and their integration with complex data, the MathSys II CDT will generate diverse impacts beyond academia. This includes impacts on skills, on the economy, on policy and on society.

Impacts on skills.
MathSys II will produce a minimum of 50 PhD graduates to support the growing national demand for advanced mathematical modelling and data analysis skills. The CDT will provide each of them with broad core skills in the MSc, a deep knowledge of their chosen research specialisation in the PhD and a complementary qualification in transferable skills integrated throughout. Graduates will thus acquire the profiles needed to form the next generation of leaders in business, government and academia. They will be supported by an integrated pastoral support framework, including a diverse group of accessible leadership role models. The cohort based environment of the CDT provides a multiplier effect by encouraging cohorts to forge long-lasting professional networks whose value and influence will long outlast the CDT itself. MathSys II will seek to maximise the influence of these networks by providing topical training in Responsible Research and Innovation, by maintaining a robust Equality, Diversity & Inclusion policy, and by integration with Warwick's global network of international partnerships.

Economic impacts.
The research outputs from many MathSys II PhD projects will be of direct economic value to commercial, public sector and charitable external partners. Engagement with CDT partners will facilitate these impacts. This includes co-supervision of PhD and MSc projects, co-creation of Research Study Groups, and a strong commitment to provide placements/internships for CDT students. When commercial innovations or IP are generated, we will work with Warwick Ventures, the commercial arm of the University of Warwick, to commercialise/license IP where appropriate. Economic impact may also come from the creation of new companies by CDT graduates. MathSys II will present entrepreneurship as a viable career option to students. One external partner, Spectra Analytics, was founded by graduates of the preceding Complexity Science CDT, thus providing accessible role models. We will also provide in-house entrepreneurship training via Warwick Ventures and host events by external start-up accelerator Entrepreneur First.

Impacts on policy.
The CDT will influence policy at the national and international level by working with external partners operating in policy. UK examples include Department of Health, Public Health England and DEFRA. International examples include World Health Organisation (WHO) and the European Commission for the Control of Foot-and-mouth Disease (EuFMD). MathSys students will also utilise the recently announced UKRI policy internships scheme.

Impacts on society.
Public engagement will allow CDT students to promote the value of their research to society at large. Aside from social media, suitable local events include DataBeers, Cafe Scientifique, and the Big Bang Fair. MathSys will also promote a socially-oriented ethos of technology for the common good. Concretely, this includes the creation of open-source software, integration of software and data carpentry into our computational and data driven research training and championing open-access to research. We will also contribute to the 'innovation culture and science' strand of Coventry's 2021 City of Culture programme.