# Prosiectau Ffiseg ar gyfer myfyrwyr bl.3 a bl.4

### From face coverings to control rods - modelling criticality

#### (supervisor: Rudi Winter)

Nature of project: theory, software

Available to students on full-time physics degree schemes or joint students.

#### Project description and methodology

When the world started to come to terms with the Covid epidemic in the spring of 2020, scientists were called on to explain what was happening and advise governments and the public on how to respond to limit the spread of the disease. Strikingly, apart from medics of various flavours, most of them were physicists. They use mathematical models and simulation techniques which are routinely used in various branches of our subject (such as nuclear fission or ionic conduction) and adapt them to understand and predict the progression of the disease under various scenarios, with constraints for their models provided by medics and sociologists.

In this project, we will investigate the analogy between nuclear chain reactions and the spread of an epidemic. Both processes proceed exponentially, governed by a reproduction number which determines whether the system is sub- or supercritical. Measures such as social distancing and the introduction of face coverings reduce the effective reproduction number of an epidemic in the same way that control rods and moderators prevent a chain reaction from running away.

The aim of the project is to develop software which enables us to model a critical process subject to such interventions. It should be sufficiently complex to model the effect of interventions of different latency (i.e. how long it takes for an intervention to kick in) and sufficiently general that it can be applied to both nuclear chain reactions and epidemics by simply relabelling the parameters. The software will be validated against epidemiological and/or nuclear data.

A successful project will develop beyond the above in one/some of the following directions:
(1) An extension of the software could attempt to model the phenomenon of super-spreading, i.e. the observation that the effective reproduction number is much higher than average in certain situations such as poorly ventilated rooms filled with many people. What is the nuclear analogy to this phenomenon?

(2) Another extension could investigate the effect of confinement of the system. In a population, there is limited scope for individuals to escape from an outbreak - there is no dilution due to radial spread from a centre. In nuclear chain reactions, geometry is of enormous importance as a series of criticality accidents in the 1950s and 1960s demonstrates. Can we learn something for handling epidemics from these observations?

(3) Once a working simulation has been developed and validated, it could be interesting to turn it into an app (e.g. an interactive web page) to enable users to explore the various parameters. This should include documentation suitable for dissemination to the general public.

When considering where to take your project, please bear in mind the time available. It is preferable to do fewer things well than to try many and not get conclusive results on any of them. However, sometimes it is useful to have a couple of strands of investigation in parallel to work on in case delays occur.

Additional scope or challenge if taken as a Year-4 project: A Y4 student should work the aspect of compliance with interventions into the model. There is no nuclear analogy to this as neutrons are not generally considered to have a free will. Does a reduced compliance rate simply reduce the effectiveness of interventions linearly or has it more complex effects?

Please speak to Rudi Winter (ruw) if you consider doing this project.

Initial literature for students:

1. M Park et al.; J Clin Med 9 (2020) 967
2. Tang Biao et al.; J Clin Med 9 (2020) 462
3. TP McLaughlin et al.; A Review of Criticality Accidents; LA-13638, Los Alamos Natl Lab (2000)

#### Novelty, degree of difficulty and amount of assistance required

The base epidemiological model for this study, the SEIR model, is long established, and coding it into a workable simulation will be straightforward. Extensions to the model need to be informed by literature and validated using published data, which requires careful analysis. The analogy with nuclear criticality is striking, but careful consideration of the limits of the analogy is needed. The student is free in their choice of programming language; help can be provided in python or C. Of the two epidemic modelling projects, this is the more straightforward one in that more of it is based on the translation of existing models into code. However, this doesn't stop an ambitious student to go well beyond the stage of pure reproduction.

#### Project milestones and deliverables (including timescale)

milestoneto be completed by
Identification of base model and a selection of interventions/extensions to be modelled.end of November
Outline of pseudo-code for the criticality model software.Christmas
Core SEIR model coded, tested and validated.end of February
Interventions/extensions of the model coded, tested and validated.Easter