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Adam Griffin


adam . griffin -obvious symbol-;
B0.12, Mathematics Institute, Zeeman Building

Currently Studying: MASDOC PhD

Undergraduate Degree: MMath from University of Warwick

Areas of Interest:

Epidemic Models - Mathematical Statistics.

Monte Carlo Simulation

Probability Theory

Current Research Interests:

I am currently working on a PhD project, supervised by Simon Spencer and Gareth Roberts regarding epidemic models, and in particular looking at quasi-stationary distributions with regards to modelling influenza infection, and how the dominating strains change over time.
This work has links to branching and birth-death processes, as well as more general characterisation of stationary distribution for Markov and non-Markov processes.

This has involved developing analytic results regarding existence and uniqueness for a class of epidemic models which incorporate transient immunity into the model. In addition I have obtained results regarding the distributions for such processes.

More recent work has centered around developing Monte Carlo methods to simulate limiting conditional distributions from intial conditions with finite support. Due to the tranisence of the processes of interest, I have be investigating stopping time resampling methods for Sequential Monte Carlo methods. We have a paper outlining Regional Resampling, and Combine-Split Resampling which more efficiently make use of particles with negligible importance weight. This also addresses issue regarding problems with resampling in reducible state spaces. This is now being applied to negelected tropical diseases through the use of Approximate Bayesian Computation.

Example of Regional Resampling

Regional Resampling

Example of Combine-Split Resampling

Combine-Split Resampling

Using the simulation methods above, I have extended the standard SIS epidemic model to include an evolving strain mechanism which allows for the continued evolution of a pathogen, such as influenza. This allows one to model immunity within a population, and the rate of evolution of the pathogen. Existence results have been obtained regarding QSDs, and the model is being studied in depth to compare to pathogens which exhibit quasi-stationary behaviour before extinction, such as seasonal influenza.

Previous Projects:

For my undergraduate project, I worked with Roger Tribe on elaborating on a paper by Volkov/Menshikov on reccurence relations in time inhomogeneous random walks on the real line (discrete time, continuous space), and developing these ideas to a continuous time setting using SDEs and Brownian Motion.

For my MSc project, I worked with Xue-Mei Li on non-linear measure-valued SDEs related to modelling granular media, and read into rates of convergence to equilibrium for solutions to such non-linear SDEs: this involved looking at the underlying semigroup theory, and on gradient flows on measure spaces.

Papers written:

Simulating Quasi-Stationary Distributions for Reducible State Spaces (2016): Griffin, A., Spencer, S.E.F., Roberts, G.O., Jenkins, P. (to be published)

Posters presented:

Simulating QSDs for Influenza Models: Epidemics Conference; Florida, USA (Dec 2015)

Quasi-stationary Distributions for Epidemic Models: MASDOC retreat (May 2014)

Spatial Lambda-Coalescent Population Genetics (May 2013)

Talks given:

Simulating Quasi-Stationary Distributions for Reducible State Spaces: RSC Leeds Conference (August 2015)

Quasi-Stationary Distributions on Reducible State Spaces: Algorithms and Computationally Intensive Inference Seminar (May 2015)

Regional Resampling for Quasi-Stationary Distributions: MASDOC Retreat (April 2015)

Simulating Quasi-Stationary Distributions for Epidemic Models: MASDOC-CCA conference 2015

Quasi-stationary Distributions for Epidemic Models: MASDOC-CCA conference 2014


SO243: Practice of Quantitative Research 2015 (Sociology)

ST202: Stochastic Processes seminar teacher 2014-15

First year mathematics supervisor: 2011-12, 2013-14

Outside of maths, I participate in the university symphony orchestra (cellist) , and the university folk society's ceilidh band (guitar/octave mandolin). I also have another folk dance band: The Night Before.