PGR Practice Talks (Nov 2022)

The SIAM & IMA Student Chapter is organising a PGR Practice Talk, giving PGR students the opportunity to present their work and ask for input from other PGR students. The event will be held on Monday the 14th of November, from 14:00-17:30 in Room D04, Monica Patridge Building (formerly known as Teaching and Learning building).

Come along and support your fellow PGRs! Drinks and Snacks will be provided.

Programme:

14:15 – Liam Critcher: The impact of household structure on herd immunity

This work concerns vaccination, in particular the use of disease-induced herd immunity; the spread of infection can be considered as a targeted vaccine, with an aim to prevent a major outbreak. The required proportion to be targeted in order to do so is referred to as the disease-induced herd immunity level. Often heterogeneity in the population can lower the disease-induced herd immunity level. We consider disease-induced herd immunity in the households model and compare it to the classical herd immunity level in which individuals are vaccinated uniformly at random among the population.

14:35 – Adam Shaw: Chiral Yang-Mills and complex Electromagnetism

14:55 – Niamh Martin: Temporal effects in epidemic modelling

15:15 – Asmaa Albuqami: Model Assessment for Stochastic Epidemic Models

In this talk, a novel method for assessing goodness-of-fit for a Susceptible-Infective-Removed (SIR) stochastic epidemic model will be discussed. The time-rescaling theorem is considered to assess the model adequacy for the Markovian SIR model. Our method assumes that the data set has been generated by the Markovian SIR model and then a vector of rescaled waiting times can be calculated using exponential distribution properties. The distribution of the rescaled waiting times is compared to the exponential distribution with rate one using the Kolmogorov-Smirnov test. The performance of our proposed method is evaluated using simulated outbreak data sets. We simulate different complete data sets from the Markovian SIR model with linear infection rate (MSIRL), the Markovian SIR model with non-linear infection rate (MSIRNL), and the non-Markovian SIR with gamma infectious period. Then, we aim to discover if our method has the ability to identify the differences between the data and the Markovian SIR models ( when the wrong model is applied to the data set). Our findings illustrate that the vector of the rescaled waiting times appears to work well as a measure of model adequacy in the case of complete data. 

10-minute break

15:45 – Adam Blakey: Placental haemodynamics: Transport effects at the organ scale

The placenta provides nutrients, such as oxygen, to developing fetuses — and is therefore vital to fetal development. It brings maternal and fetal blood close together, allowing nutrients to diffuse across thin separating barriers in the fetal arterial tree structure. Structurally, the placenta is divided into placentones: compartments that are partially separated by so-called septal walls. An approach to modelling maternal blood flow is to treat the fetal arterial tree as a porous medium; several authors have utilised this on representative placentone geometries, mainly focusing on arterial supply. However, whilst these simulations are a useful indicator of organ-level behaviour, they fail to describe the effects of the blood flux between neighbouring placentones, as well as neglecting the importance of maternal venous return. In 2020, a new phenomenon was discovered called the placental contraction, which is yet to be mathematically modelled. I will present some in-silico organ-scale maternal blood flow simulations, which use discontinuous Galerkin finite element methods (DGFEMs), on the Brinkman equation to model blood flow on representative placental geometries, coupled to a reaction-advection-diffusion equation to model nutrient transport. I will show notable blood flux passing between placentones, the importance of including maternal venous return on the uniformity of nutrient exchange, and how the recently-observed placental contraction phenomena could be vital in redistributing blood and encouraging venous return.

16:05 – Sonia Dari: Modelling the role of Matrix Metalloproteinases in the persistence of chronic wounds

Treating chronic wounds is a developing area of research; as such, understanding the biochemistry and pharmacology that underpins wound healing is of high importance. Biological research suggests that one such cause for the emergence of chronic wounds is deregulated apoptosis. In particular, chronic wounds are particularly susceptible to high levels of Matrix Metalloproteinases (MMPs), which cease to be beneficial and cause destruction of the extracellular matrix (ECM). In this talk, we propose a mathematical model that focuses on the interaction of MMPs with the ECM using a system of partial
differential equations. We examine the qualitative features of the resulting travelling wave solutions observed in using parameters for healthy biological functioning and observe how these change for varying apoptotic rates.

16:25 – Alice Thompson: Multi-strain models for nosocomial infections featuring environmental transmission

Nosocomial infections have been a growing problem in hospitals for over 50 years, with most of these infections being due to the introduction and misuse of antibiotics. With motivation from a unique data set, this talk discusses how transmission networks can be reconstructed for a multi-strain outbreak in a hospital environment. This research focuses on the use of genetic data, collected using Whole Genome Sequencing techniques, and epidemiological data from patients and surfaces to reconstruct transmission networks of various stains and species of Klebsiella pneumoniae Carbapenemase (KPC)-producing bacteria. In this talk, we will first introduce the data set and then discuss the multi-strain transmission model and its augmented likelihood. Next, we discuss the use of MCMC and data augmentation, and the results yielded when using this method on a simulated data set. Finally a new model will be introduced which also incorporates environmental data and enables environment to be part of the transmission network.

16:45 – Jiale Tao: Bayesian Detection and Prediction of Disruptive Events in Twitter Data

The volume of tweets on Twitter is increasing exponentially, thus providing us with numerous opportunities for detecting the occurrence of major events in real-time. We develop a state-space model for detecting disruption on the National Railway in Great Britain in a timely fashion, by using the content and volume of tweets referring to delays and disturbance in the railway. A time-inhomogeneous Poisson process, lambda(t), is proposed to model the number of tweets whose time-dependent intensity function is parameterized such that it captures the observed periodic pattern in the data. A hidden Markov process that represents the state of the railway through time (‘normal’/ ‘abnormal’) then modulates the Poisson process. We develop a computationally efficient MCMC algorithm to learn the parameters governing lambda(t) and infer the state of the railway through time by utilizing a Forward-Backward algorithm to efficiently update the unobserved process. We demonstrate through extensive simulation studies that (i) we can successfully recover the model’s unknown parameters, (ii) predict the unobserved state with high accuracy framework our results are robust model misspecification. Finally, we illustrate via Bayesian filtering how to predict the future state of railway in real-time given the observed number of tweets.