Description

There are many physical systems that scientists aim to understand, including the outbreak and spread of COVID-19 through a population.  A crucial aspect of understanding such systems is construction of a complex computer model, which in this case seek to describe the major epidemiological processes thought to underpin COVID-19 transmission.  Such models typically represent the system as execution of computer code, for example, numerically solving sets of differential equations.  These equations are usually determined by sets of rate parameters, for example, representing the rates of infection of the virus.

This project aims to investigate simulation of compartmental COVID-19 models for the purpose of making inferences about their rate parameters, and hence corresponding properties of COVID-19 transmission, by matching model output to data using Approximate Bayesian Computation (ABC).  ABC is an approximate method for Bayesian inference when the likelihood is analytically intractable (which is often the case unless I make overly simplifying assumptions regarding tractable probability distributions).  Suffice it to say that if a complex computer model is the one I want to use to answer the right question, then I prefer to obtain an approximative answer using approximate inference than fooling myself with a simpler model using exact inference.

The possible directions for this project are diverse, including analysis of various interventions (e.g. lockdown) through additional model compartments, particularly as a response to possible virus mutations and vaccination efficacy.  Substantial coding (for example, in R) will be necessary to practically carry out and investigate both COVID-19 models and ABC.

Prerequisites

• Statistical Inference II
• Data Science and Statistical Computing II
• Statistical Modelling II

Resources

·       A good site that makes you aware of the standard traps modellers fall into is Epidemic Modelling 101: Or why your CoVID-19 exponential fits are wrong, but do be aware that we will go much further than the models discussed here.

·       A couple of websites introducing the notion of ABC can be found here

o   The ABCs of ABC

o   Introduction to Approximate Bayesian Computation (ABC)

·       For an academic paper looking into applying ABC to models including compartmental SIR-type models, see Toni et al. (2009): Approximate Bayesian computation scheme for parameter inference and model selection in dynamical systems, Journal of the Royal Society Interface.