arXiv subjects

Thomas A. Mellan

Publications and source records attributed to Thomas A. Mellan.

10 recordsLinked to original sources

arXiv2022

Unifying incidence and prevalence under a time-varying general branching process

Renewal equations are a popular approach used in modelling the number of new infections, i.e., incidence, in an outbreak. We develop a stochastic model of an outbreak based on a time-varying variant of the Crump-Mode-Jagers branching process. This model accommodates a time-varying reproduction number and a time-varying distribution for the generation interval. We then derive renewal-like integral equations for incidence, cumulative incidence and prevalence under this model. We show that the equations for incidence and prevalence are consistent with the so-called back-calculation relationship. We analyse two particular cases of these integral equations, one that arises from a Bellman-Harris process and one that arises from an inhomogeneous Poisson process model of transmission. We also show that the incidence integral equations that arise from both of these specific models agree with the renewal equation used ubiquitously in infectious disease modelling. We present a numerical discretisation scheme to solve these equations, and use this scheme to estimate rates of transmission from serological prevalence of SARS-CoV-2 in the UK and historical incidence data on Influenza, Measles, SARS and Smallpox.

q-bio.PE↗

arXiv2021

Referenced Thermodynamic Integration for Bayesian Model Selection: Application to COVID-19 Model Selection

Model selection is a fundamental part of the applied Bayesian statistical methodology. Metrics such as the Akaike Information Criterion are commonly used in practice to select models but do not incorporate the uncertainty of the models' parameters and can give misleading choices. One approach that uses the full posterior distribution is to compute the ratio of two models' normalising constants, known as the Bayes factor. Often in realistic problems, this involves the integration of analytically intractable, high-dimensional distributions, and therefore requires the use of stochastic methods such as thermodynamic integration (TI). In this paper we apply a variation of the TI method, referred to as referenced TI, which computes a single model's normalising constant in an efficient way by using a judiciously chosen reference density. The advantages of the approach and theoretical considerations are set out, along with explicit pedagogical 1 and 2D examples. Benchmarking is presented with comparable methods and we find favourable convergence performance. The approach is shown to be useful in practice when applied to a real problem - to perform model selection for a semi-mechanistic hierarchical Bayesian model of COVID-19 transmission in South Korea involving the integration of a 200D density.

stat.AP↗

arXiv2020

Inference of COVID-19 epidemiological distributions from Brazilian hospital data

Knowing COVID-19 epidemiological distributions, such as the time from patient admission to death, is directly relevant to effective primary and secondary care planning, and moreover, the mathematical modelling of the pandemic generally. We determine epidemiological distributions for patients hospitalised with COVID-19 using a large dataset ($N=21{,}000-157{,}000$) from the Brazilian Sistema de Informação de Vigilância Epidemiológica da Gripe database. A joint Bayesian subnational model with partial pooling is used to simultaneously describe the 26 states and one federal district of Brazil, and shows significant variation in the mean of the symptom-onset-to-death time, with ranges between 11.2-17.8 days across the different states, and a mean of 15.2 days for Brazil. We find strong evidence in favour of specific probability density function choices: for example, the gamma distribution gives the best fit for onset-to-death and the generalised log-normal for onset-to-hospital-admission. Our results show that epidemiological distributions have considerable geographical variation, and provide the first estimates of these distributions in a low and middle-income setting. At the subnational level, variation in COVID-19 outcome timings are found to be correlated with poverty, deprivation and segregation levels, and weaker correlation is observed for mean age, wealth and urbanicity.

q-bio.PE↗

arXiv2020

A unified machine learning approach to time series forecasting applied to demand at emergency departments

There were 25.6 million attendances at Emergency Departments (EDs) in England in 2019 corresponding to an increase of 12 million attendances over the past ten years. The steadily rising demand at EDs creates a constant challenge to provide adequate quality of care while maintaining standards and productivity. Managing hospital demand effectively requires an adequate knowledge of the future rate of admission. Using 8 years of electronic admissions data from two major acute care hospitals in London, we develop a novel ensemble methodology that combines the outcomes of the best performing time series and machine learning approaches in order to make highly accurate forecasts of demand, 1, 3 and 7 days in the future. Both hospitals face an average daily demand of 208 and 106 attendances respectively and experience considerable volatility around this mean. However, our approach is able to predict attendances at these emergency departments one day in advance up to a mean absolute error of +/- 14 and +/- 10 patients corresponding to a mean absolute percentage error of 6.8% and 8.6% respectively. Our analysis compares machine learning algorithms to more traditional linear models. We find that linear models often outperform machine learning methods and that the quality of our predictions for any of the forecasting horizons of 1, 3 or 7 days are comparable as measured in MAE. In addition to comparing and combining state-of-the-art forecasting methods to predict hospital demand, we consider two different hyperparameter tuning methods, enabling a faster deployment of our models without compromising performance. We believe our framework can readily be used to forecast a wide range of policy relevant indicators.

stat.AP↗

arXiv2020

On the derivation of the renewal equation from an age-dependent branching process: an epidemic modelling perspective

Renewal processes are a popular approach used in modelling infectious disease outbreaks. In a renewal process, previous infections give rise to future infections. However, while this formulation seems sensible, its application to infectious disease can be difficult to justify from first principles. It has been shown from the seminal work of Bellman and Harris that the renewal equation arises as the expectation of an age-dependent branching process. In this paper we provide a detailed derivation of the original Bellman Harris process. We introduce generalisations, that allow for time-varying reproduction numbers and the accounting of exogenous events, such as importations. We show how inference on the renewal equation is easy to accomplish within a Bayesian hierarchical framework. Using off the shelf MCMC packages, we fit to South Korea COVID-19 case data to estimate reproduction numbers and importations. Our derivation provides the mathematical fundamentals and assumptions underpinning the use of the renewal equation for modelling outbreaks.

q-bio.PE↗

arXiv2019

A fast anharmonic free energy method with an application to vacancies in ZrC

We propose an approach to calculate the anharmonic part of the volumetric-strain and temperature dependent free energy of a crystal. The method strikes an effective balance between accuracy and computational efficiency, showing a $\times10$ speed-up on comparable free energy approaches at the level of density functional theory, with average errors less than 1 meV/atom. As a demonstration we make new predictions on the thermodynamics of substoichiometric ZrC$_x$, including vacancy concentration and heat capacity.

cond-mat.mtrl-sci↗

arXiv2019

Electron and phonon interactions and transport in ultra-high-temperature ceramic ZrC

We have simulated the ultra-high-temperature ceramic zirconium carbide (ZrC) in order to predict electron and phonon scattering properties, including lifetimes and transport. Our predictions of heat and charge conductivity, which extend to 3000 K, are relevant to extreme temperature applications of ZrC. Mechanisms are identified on a first principles basis that considerably enhance or suppress heat transport at high temperature, including strain and anharmonicity. The extent to which boundary confinement and isotope scattering effects lower thermal conductivity is predicted.

cond-mat.mtrl-sci↗

arXiv2018

Spontaneous Frenkel pair formation in Zirconium Carbide

With density functional theory we have performed molecular dynamics simulations of ZrC which displayed spontaneous Frenkel pair formation at a temperature of 3200 K, some 500 K below the melting point. To understand this behaviour, rarely seen in equilibrium simulations, we quenched and examined a set of lattices containing a Frenkel pair. Five metastable structures were found, and their formation energies and electronic properties were studied. Their thermal generation was found to be facilitated by a reduction of between 0.7 and 1.5 eV in formation energy due to thermal expansion of the lattice. With input from a quasi-harmonic description of the defect free energy of formation, an ideal solution model was used to estimate lower bounds on their concentration as a function of temperature and stoichiometry. At 3000 K (0.81 of the melting temperature) their concentration was estimated to be 1.2% per mole in a stoichiometric crystal, and 0.3% per mole in a crystal with 10% per mole of constitutional vacancies. Their contribution to heat capacity, thermal expansion and bulk modulus was estimated.

cond-mat.mtrl-sci↗

arXiv2015

The importance of anisotropic Coulomb interaction in LaMnO$_{3}$

In low-temperature anti-ferromagnetic LaMnO$_{3}$, strong and localized electronic interactions among Mn 3d electrons prevent a satisfactory description from standard local density and generalized gradient approximations in density functional theory calculations. Here we show that the strong on-site electronic interactions are described well only by using direct and exchange corrections to the intra-orbital Coulomb potential. Only DFT+U calculations with explicit exchange corrections produce a balanced picture of electronic, magnetic and structural observables in agreement with experiment. To understand the reason, a rewriting of the functional form of the +U corrections is presented that leads to a more physical and transparent understanding of the effect of these correction terms. The approach highlights the importance of Hund's coupling (intra-orbital exchange) in providing anisotropy across the occupation and energy eigenvalues of the Mn d states. This intra-orbital exchange is the key to fully activating the Jahn-Teller distortion, reproducing the experimental band gap and stabilizing the correct magnetic ground state in LaMnO$_{3}$. The best parameter values for LaMnO$_{3}$ within the DFT (PBEsol) +U framework are determined to be U = 8 eV and J = 1.9 eV.

cond-mat.mtrl-sci↗

arXiv2012

Density functional theory study of rutile VO2 surfaces

We present the results of a density functional theory (DFT) investigation of the surfaces of rutile-like vanadium dioxide, VO2(R). We calculate the surface energies of low Miller index planes, and find that the most stable surface orientation is the (110). The equilibrium morphology of a VO2(R) particle has an acicular shape, laterally confined by (110) planes and topped by (011) planes. The redox properties of the (110) surface are investigated by calculating the relative surface free energies of the non-stoichiometric compositions as a function of oxygen chemical potential. It is found that the VO2(110) surface is oxidized with respect to the stoichiometric composition, not only at ambient conditions but also at the more reducing conditions under which bulk VO2 is stable in comparison with bulk V2O5. The adsorbed oxygen forms surface vanadyl species much more favorably than surface peroxo species.

physics.chem-ph↗