Bayesian Evidence Synthesis for Modeling SARS-CoV-2 Transmission

The acute phase of the Covid-19 pandemic has made apparent the need for decision support based upon accurate epidemic modeling. This process is substantially hampered by under-reporting of cases and related data incompleteness issues. In this article, a discrete-time stochastic epidemic modeling framework is developed with discernible features targeted to publicly available data. The models allow for estimating the total number of infections while accounting for the endemic phase of the pandemic. We assess the prediction of the infection rate utilizing mobility information, notably the principal components of the mobility data. We elaborate upon vector analysis of the epidemic dynamics, thus enriching the traditional tools used for decision making. In particular, we show how certain 2-dimensional plots on the phase plane may yield intuitive information regarding the speed and the type of transmission dynamics.Comment: 32 pages, 6 figure

Multiphasic stochastic epidemic models

At the onset of the Covid-19 pandemic, a number of non-pharmaceutical interventions have been implemented in order to reduce transmission, thus leading to multiple phases of transmission. The disease reproduction number $R_t$, a way of quantifying transmissibility, has been a key part in assessing the impact of such interventions. We discuss the distinct types of transmission models used and how they are linked. We consider a hierarchical stochastic epidemic model with piece-wise constant $R_t$, appropriate for modelling the distinct phases of the epidemic and quantifying the true disease magnitude. The location and scale of $R_t$ changes are inferred directly from data while the number of transmissibility phases is allowed to vary. We determine the model complexity via appropriate Poisson point process and Dirichlet process-type modelling components. The models are evaluated using synthetic data sets and the methods are applied to freely available data from California and New York states as well as the United Kingdom and Greece. We estimate the true infected cases and the corresponding $R_t$, among other quantities, and independently validate the proposed approach using a large seroprevalence study

Bayesian Inference for Stochastic Epidemic Models using Markov chain Monte Carlo Methods

This thesis is concerned with statistical methodology for the analysis of stochastic SIR (Susceptible->Infective->Removed) epidemic models. We adopt the Bayesian paradigm and we develop suitably tailored Markov chain Monte Carlo (MCMC) algorithms. The focus is on methods that are easy to generalise in order to accomodate epidemic models with complex population structures. Additionally, the models are general enough to be applicable to a wide range of infectious diseases. We introduce the stochastic epidemic models of interest and the MCMC methods we shall use and we review existing methods of statistical inference for epidemic models. We develop algorithms that utilise multiple precision arithmetic to overcome the well-known numerical problems in the calculation of the final size distribution for the generalised stochastic epidemic. Consequently, we use these exact results to evaluate the precision of asymptotic theorems previously derived in the literature. We also use the exact final size probabilities to obtain the posterior distribution of the threshold parameter $R_0$. We proceed to develop methods of statistical inference for an epidemic model with two levels of mixing. This model assumes that the population is partitioned into subpopulations and permits infection on both local (within-group) and global (population-wide) scales. We adopt two different data augmentation algorithms. The first method introduces an appropriate latent variable, the \emph{final severity}, for which we have asymptotic information in the event of an outbreak among a population with a large number of groups. Hence, approximate inference can be performed conditional on a ``major'' outbreak, a common assumption for stochastic processes with threshold behaviour such as epidemics and branching processes. In the last part of this thesis we use a \emph{random graph} representation of the epidemic process and we impute more detailed information about the infection spread. The augmented state-space contains aspects of the infection spread that have been impossible to obtain before. Additionally, the method is exact in the sense that it works for any (finite) population and group sizes and it does not assume that the epidemic is above threshold. Potential uses of the extra information include the design and testing of appropriate prophylactic measures like different vaccination strategies. An attractive feature is that the two algorithms complement each other in the sense that when the number of groups is large the approximate method (which is faster) is almost as accurate as the exact one and can be used instead. Finally, it is straightforward to extend our methods to more complex population structures like overlapping groups, small-world and scale-free network

Bayesian Inference for Stochastic Epidemic Models using Markov chain Monte Carlo Methods

This thesis is concerned with statistical methodology for the analysis of stochastic SIR (Susceptible->Infective->Removed) epidemic models. We adopt the Bayesian paradigm and we develop suitably tailored Markov chain Monte Carlo (MCMC) algorithms. The focus is on methods that are easy to generalise in order to accomodate epidemic models with complex population structures. Additionally, the models are general enough to be applicable to a wide range of infectious diseases. We introduce the stochastic epidemic models of interest and the MCMC methods we shall use and we review existing methods of statistical inference for epidemic models. We develop algorithms that utilise multiple precision arithmetic to overcome the well-known numerical problems in the calculation of the final size distribution for the generalised stochastic epidemic. Consequently, we use these exact results to evaluate the precision of asymptotic theorems previously derived in the literature. We also use the exact final size probabilities to obtain the posterior distribution of the threshold parameter $R_0$. We proceed to develop methods of statistical inference for an epidemic model with two levels of mixing. This model assumes that the population is partitioned into subpopulations and permits infection on both local (within-group) and global (population-wide) scales. We adopt two different data augmentation algorithms. The first method introduces an appropriate latent variable, the \emph{final severity}, for which we have asymptotic information in the event of an outbreak among a population with a large number of groups. Hence, approximate inference can be performed conditional on a ``major'' outbreak, a common assumption for stochastic processes with threshold behaviour such as epidemics and branching processes. In the last part of this thesis we use a \emph{random graph} representation of the epidemic process and we impute more detailed information about the infection spread. The augmented state-space contains aspects of the infection spread that have been impossible to obtain before. Additionally, the method is exact in the sense that it works for any (finite) population and group sizes and it does not assume that the epidemic is above threshold. Potential uses of the extra information include the design and testing of appropriate prophylactic measures like different vaccination strategies. An attractive feature is that the two algorithms complement each other in the sense that when the number of groups is large the approximate method (which is faster) is almost as accurate as the exact one and can be used instead. Finally, it is straightforward to extend our methods to more complex population structures like overlapping groups, small-world and scale-free network

Assessing optimal target populations for influenza vaccination programmes: an evidence synthesis and modelling study.

BACKGROUND: Influenza vaccine policies that maximise health benefit through efficient use of limited resources are needed. Generally, influenza vaccination programmes have targeted individuals 65 y and over and those at risk, according to World Health Organization recommendations. We developed methods to synthesise the multiplicity of surveillance datasets in order to evaluate how changing target populations in the seasonal vaccination programme would affect infection rate and mortality. METHODS AND FINDINGS: Using a contemporary evidence-synthesis approach, we use virological, clinical, epidemiological, and behavioural data to develop an age- and risk-stratified transmission model that reproduces the strain-specific behaviour of influenza over 14 seasons in England and Wales, having accounted for the vaccination uptake over this period. We estimate the reduction in infections and deaths achieved by the historical programme compared with no vaccination, and the reduction had different policies been in place over the period. We find that the current programme has averted 0.39 (95% credible interval 0.34-0.45) infections per dose of vaccine and 1.74 (1.16-3.02) deaths per 1,000 doses. Targeting transmitters by extending the current programme to 5-16-y-old children would increase the efficiency of the total programme, resulting in an overall reduction of 0.70 (0.52-0.81) infections per dose and 1.95 (1.28-3.39) deaths per 1,000 doses. In comparison, choosing the next group most at risk (50-64-y-olds) would prevent only 0.43 (0.35-0.52) infections per dose and 1.77 (1.15-3.14) deaths per 1,000 doses. CONCLUSIONS: This study proposes a framework to integrate influenza surveillance data into transmission models. Application to data from England and Wales confirms the role of children as key infection spreaders. The most efficient use of vaccine to reduce overall influenza morbidity and mortality is thus to target children in addition to older adults. Please see later in the article for the Editors' Summary

Modeling sheep pox disease from the 1994-1998 epidemic in Evros Prefecture, Greece.

Sheep pox is a highly transmissible disease which can cause serious loss of livestock and can therefore have major economic impact. We present data from sheep pox epidemics which occurred between 1994 and 1998. The data include weekly records of infected farms as well as a number of covariates. We implement Bayesian stochastic regression models which, in addition to various explanatory variables like seasonal and environmental/meteorological factors, also contain serial correlation structure based on variants of the Ornstein–Uhlenbeck process. We take a predictive view in model selection by utilizing deviance-based measures. The results indicate that seasonality and the number of infected farms are important predictors for sheep pox incidence

On the epidemic of financial crises

The paper proposes a framework for modelling financial contagion that is based on susceptible-infected-recovered transmission models from epidemic theory. This class of models addresses two important features of contagion modelling, which are a common shortcoming of most existing empirical approaches, namely the direct modelling of the inherent dependences that are involved in the transmission mechanism, and an associated canonical measure of crisis severity. The methodology proposed naturally implies a control mechanism, which is required when evaluating prospective immunization policies that intend to mitigate the effect of a crisis. It can be implemented not only as a way of learning from past experiences, but also at the onset of a contagious financial crisis. The approach is illustrated on a number of currency crisis episodes, using both historical final outcome and temporal data. The latter require the introduction of a novel hierarchical model that we call the hidden epidemic model and which embeds the stochastic financial epidemic as a latent process. The empirical results suggest, among others, an increasing trend for global transmission of currency crises over time. © 2013 Royal Statistical Society

On the epidemic of financial crises

This paper proposes a framework for modelling financial contagion that is based on SIR (Susceptible-Infected-Recovered) transmission models from epidemic theory. This class of models addresses two important features of contagion modelling, which are a common shortcoming of most existing empirical approaches, namely the direct modelling of the inherent dependencies involved in the transmission mechanism, and an associated canonical measure of crisis severity. The proposed methodology naturally implies a control mechanism, which is required when evaluating prospective immunisation policies that intend to mitigate the impact of a crisis. It can be implemented not only as a way of learning from past experiences, but also at the onset of a contagious financial crisis. The approach is illustrated on a number of currency crisis episodes, using both historical final outcome and temporal data. The latter require the introduction of a novel hierarchical model that we call the Hidden Epidemic Model (HEM), and which embeds the stochastic financial epidemic as a latent process. The empirical results suggest, among others, an increasing trend for global transmission of currency crises over time

Survival extrapolation using the poly-Weibull model.

Recent studies of (cost-) effectiveness in cardiothoracic transplantation have required estimation of mean survival over the lifetime of the recipients. In order to calculate mean survival, the complete survivor curve is required but is often not fully observed, so that survival extrapolation is necessary. After transplantation, the hazard function is bathtub-shaped, reflecting latent competing risks which operate additively in overlapping time periods. The poly-Weibull distribution is a flexible parametric model that may be used to extrapolate survival and has a natural competing risks interpretation. In addition, treatment effects and subgroups can be modelled separately for each component of risk. We describe the model and develop inference procedures using freely available software. The methods are applied to two problems from cardiothoracic transplantation

A quantitative analysis of the spatial and temporal evolution patterns of the bluetongue virus outbreak in the island of Lesvos, Greece in 2014

Bluetongue virus (BTV) causes an infectious disease called bluetongue, a vector-borne viral disease of ruminants, which has major implications and causes severe economic damage due to its effect on livestock. These economic costs are mostly ascribed to the trade restrictions imposed during the epidemic period. In August 2014, an epidemic of bluetongue occurred in the island of Lesvos, Greece. The epidemic was severe and evolved over time, lasting until December 2014. The total cases of infected farms were 490, including a total number of 136,368 small ruminants. In this paper, we describe a bluetongue virus serotype 4 (BTV-4) epidemic and utilize Bayesian epidemic models to capture the spatio-temporal spread of the disease. Our study provides important insights into the drivers of BTV transmission and has implications for designing control strategies. The results showed strong spatial autocorrelations, with BTV being more likely to spread between farms located nearby. The spatial modelling results proposed a certain spatial radius (~12 km) around the onset of a similar epidemic for imposing restrictions on animal movement, which can be sufficient for the control of the disease and limit economic damage