Hierarchical space-time modelling of epidemic dynamics: an application to measles outbreaks

How infectious diseases spread in space and time is an important question that has received considerable theoretical attention. There are, however, few empirical studies to support theoretical approaches, because data is scarce. In this paper we propose to model the epidemic spread of measles in the London boroughs between 1960 and 1970 by an extension of the Kriged Kalman filter (Mardia et al. , 1998) to count data. Results show the flexibility of our approach in describing complex spatio-temporal dynamics.     

Spatio-temporal analysis of a plant disease in a non-uniform crop: a Monte Carlo approach

Identification of the type of disease pattern and spread in a field is critical in epidemiological investigations of plant diseases. For example, an aggregation pattern of infected plants suggests that, at the time of observation, the pathogen is spreading from a proximal source. Conversely, a random pattern suggests a lack of spread from a proximal source. Most of the existing methods of spatial pattern analysis work with only one variety of plant at each location and with uniform genetic disease susceptibility across the field. Pecan orchards, used in this study, and other orchard crops are usually composed of different varieties with different levels of susceptibility to disease. A new measure is suggested to characterize the spatio-temporal transmission patterns of disease; a Monte Carlo test procedure is proposed to test whether the transmission of disease is random or aggregated. In addition, we propose a mixed-transmission model, which allows us to quantify the degree of aggregation effect.     

Bayesian estimation for percolation models of disease spread in plant populations

Statistical methods are formulated for fitting and testing percolation-based, spatio-temporal models that are generally applicable to biological or physical processes that evolve in spatially distributed populations. The approach is developed and illustrated in the context of the spread of Rhizoctonia solani, a fungal pathogen, in radish but is readily generalized to other scenarios. The particular model considered represents processes of primary and secondary infection between nearest-neighbour hosts in a lattice, and time-varying susceptibility of the hosts. Bayesian methods for fitting the model to observations of disease spread through space and time in replicate populations are developed. These use Markov chain Monte Carlo methods to overcome the problems associated with partial observation of the process. We also consider how model testing can be achieved by embedding classical methods within the Bayesian analysis. In particular we show how a residual process, with known sampling distribution, can be defined. Model fit is then examined by generating samples from the posterior distribution of the residual process, to which a classical test for consistency with the known distribution is applied, enabling the posterior distribution of the P-value of the test used to be estimated. For the Rhizoctonia-radish system the methods confirm the findings of earlier non-spatial analyses regarding the dynamics of disease transmission and yield new evidence of environmental heterogeneity in the replicate experiments.     

Estimating the transmission probability of human immunodeficiency virus in injecting drug users in Thailand

We estimate the transmission probability for the human immunodeficiency virus from seroconversion data of a cohort of injecting drug users (IDUs) in Thailand. The transmission probability model developed accounts for interval censoring and incorporates each IDU's reported frequency of needle sharing and injecting acts. Using maximum likelihood methods, the per needle sharing act transmission probability estimate between infectious and susceptible IDUs is 0.008. The effects of covariates, disease dynamics, mismeasured exposure information and the uncertainty of the disease prevalence on the transmission probability estimate are considered.     

An endemic–epidemic beta model for time series of infectious disease proportions

Time series of proportions of infected patients or positive specimens are frequently encountered in disease control and prevention. Since proportions are bounded and often asymmetrically distributed, conventional Gaussian time series models only apply to suitably transformed proportions. Here we borrow both from beta regression and from the well-established HHH model for infectious disease counts to propose an endemic–epidemic beta model for proportion time series. It accommodates the asymmetric shape and heteroskedasticity of proportion distributions and is consistent for complementary proportions. Coefficients can be interpreted in terms of odds ratios. A multivariate formulation with spatial power-law weights enables the joint estimation of model parameters from multiple regions. In our application to a flu activity index in the USA, we find that the endemic–epidemic beta model provides a better fit than a seasonal ARIMA model for the logit-transformed proportions. Furthermore, a multivariate approach can improve regional forecasts and reduce model complexity in comparison to univariate beta models stratified by region.     

ANALYSIS OF DATA FROM A SINGLE EPIDEMIC1

A model with nonrandom latent and infectious periods is suggested for epidemics in a large community. This permits a relatively complete statistical analysis of data from the spread of a single epidemic. An attractive feature of such models is the possibility of exploring how the rate of spread of the disease depends on the number of susceptibles and infectives. An application to smallpox data is included.     

Individual-level modeling of the spread of influenza within households

A class of individual-level models (ILMs) outlined by R. Deardon et al., [Inference for individual level models of infectious diseases in large populations, Statist. Sin. 20 (2010), pp. 239–261] can be used to model the spread of infectious diseases in discrete time. The key feature of these ILMs is that they take into account covariate information on susceptible and infectious individuals as well as shared covariate information such as geography or contact measures. Here, such ILMs are fitted in a Bayesian framework using Markov chain Monte Carlo techniques to data sets from two studies on influenza transmission within households in Hong Kong during 2008 to 2009 and 2009 to 2010. The focus of this paper is to estimate the effect of vaccination on infection risk and choose a model that best fits the infection data.     

A random effects model for diseases with heterogeneous rates of infection

One form of data collected in the study of infectious diseases is on the transmission of a disease within households. We consider a model which allows the rate of disease transmission to vary between households. A Bayesian hierarchical approach to fitting the model is proposed and is implemented by the Metropolis–Hastings algorithm, a standard Markov chain Monte Carlo (MCMC) method. Results are presented for both simulated epidemic chain data and the Providence measles data, illustrating the potential that MCMC methods have to dealing with heterogeneity in infectious disease transmission.     

Spatio-temporal modeling of infectious disease dynamics

A stochastic model, which is well suited to capture space–time dependence of an infectious disease, was employed in this study to describe the underlying spatial and temporal pattern of measles in Barisal Division, Bangladesh. The model has two components: an endemic component and an epidemic component; weights are used in the epidemic component for better accounting of the disease spread into different geographical regions. We illustrate our findings using a data set of monthly measles counts in the six districts of Barisal, from January 2000 to August 2009, collected from the Expanded Program on Immunization, Bangladesh. The negative binomial model with both the seasonal and autoregressive components was found to be suitable for capturing space–time dependence of measles in Barisal. Analyses were done using general optimization routines, which provided the maximum likelihood estimates with the corresponding standard errors.     

Spatial measurement error in infectious disease models

Individual-level models (ILMs) for infectious disease can be used to model disease spread between individuals while taking into account important covariates. One important covariate in determining the risk of infection transfer can be spatial location. At the same time, measurement error is a concern in many areas of statistical analysis, and infectious disease modelling is no exception. In this paper, we are concerned with the issue of measurement error in the recorded location of individuals when using a simple spatial ILM to model the spread of disease within a population. An ILM that incorporates spatial location random effects is introduced within a hierarchical Bayesian framework. This model is tested upon both simulated data and data from the UK 2001 foot-and-mouth disease epidemic. The ability of the model to successfully identify both the spatial infection kernel and the basic reproduction number (R ₀) of the disease is tested.     

Inference in disease transmission experiments by using stochastic epidemic models

Summary.  The paper extends the susceptible–exposed–infective–removed model to handle heterogeneity introduced by spatially arranged populations, biologically plausible distributional assumptions and incorporation of observations from additional diagnostic tests. These extensions are motivated by a desire to analyse disease transmission experiments in a more detailed fashion than before. Such experiments are performed by veterinarians to gain knowledge about the dynamics of an infectious disease. By fitting our spatial susceptible–exposed–infective–removed with diagnostic testing model to data for a specific disease and production environment a valuable decision support tool is obtained, e.g. when evaluating on-farm control measures. Partial observability of the epidemic process is an inherent problem when trying to estimate model parameters from experimental data. We therefore extend existing work on Markov chain Monte Carlo estimation in partially observable epidemics to the multitype epidemic set-up of our model. Throughout the paper, data from a Belgian classical swine fever virus transmission experiment are used as a motivating example.     

银行风险传染随机模型研究

借鉴生物学中传染病模型,建立了银行风险传染的随机模型。描述了银行风险在银行系统中的传染过程,分析了受传染银行的数目变化规律以及银行风险传染率、银行间的关联度和银行风险治理率对银行风险传染的影响。分析结果表明：通过降低传染率、降低关联度或增加治理率都可以控制银行风险的传染,并且降低银行间的关联度比增加治理率对控制银行风险传染的效果更好。     

Modeling Competing Infectious Pathogens from a Bayesian Perspective: Application to Influenza Studies with Incomplete Laboratory Results

In seasonal influenza epidemics, pathogens such as respiratory syncytial virus (RSV) often co-circulate with influenza and cause influenza-like illness (ILI) in human hosts. However, it is often impractical to test for each potential pathogen or to collect specimens for each observed ILI episode, making inference about influenza transmission difficult. In the setting of infectious diseases, missing outcomes impose a particular challenge because of the dependence among individuals. We propose a Bayesian competing-risk model for multiple co-circulating pathogens for inference on transmissibility and intervention efficacies under the assumption that missingness in the biological confirmation of the pathogen is ignorable. Simulation studies indicate a reasonable performance of the proposed model even if the number of potential pathogens is misspecified. They also show that a moderate amount of missing laboratory test results has only a small impact on inference about key parameters in the setting of close contact groups. Using the proposed model, we found that a non-pharmaceutical intervention is marginally protective against transmission of influenza A in a study conducted in elementary schools.     

Multiple non linear regression model for the maximum number of migratory bird types during migration years

Since many years scientists have carried out researches about bird migration, but due to the large number of bird types estimated at around 10,000 in the world, it is not easy to predict the maximum number of migratory bird types through limited number of migration years. In this study, a multiple non linear regression model of maximum number probability function of migratory bird types has been obtained and can be used in the prediction of the maximum number of migratory bird types during any migration years.     

Statistical analysis of an endemic disease from a capture–recapture experiment

There are a number of statistical techniques for analysing epidemic outbreaks. However, many diseases are endemic within populations and the analysis of such diseases is complicated by changing population demography. Motivated by the spread of cowpox amongst rodent populations, a combined mathematical model for population and disease dynamics is introduced. A Markov chain Monte Carlo algorithm is then constructed to make statistical inference for the model based on data being obtained from a capture–recapture experiment. The statistical analysis is used to identify the key elements in the spread of the cowpox virus.     

Design issues for studies of infectious diseases

The design of infectious disease studies has received little attention because they are generally viewed as observational studies. That is, epidemic and endemic disease transmission happens and we observe it. We argue here that statistical design often provides useful guidance for such studies with regard to type of data and the size of the data set to be collected. It is shown that data on disease transmission in part of the community enables the estimation of central parameters and it is possible to compute the sample size required to make inferences with a desired precision. We illustrate this for data on disease transmission in a single community of uniformly mixing individuals and for data on outbreak sizes in households. Data on disease transmission is usually incomplete and this creates an identifiability problem for certain parameters of multitype epidemic models. We identify designs that can overcome this problem for the important objective of estimating parameters that help to assess the effectiveness of a vaccine. With disease transmission in animal groups there is greater scope for conducting planned experiments and we explore some possibilities for such experiments. The topic is largely unexplored and numerous open research problems in the area of statistical design of infectious disease data are mentioned.     

Statement of Withdrawal: Statistical analysis of an endemic disease from a capture–recapture experiment

There are a number of statistical techniques for analysing epidemic outbreaks. However, many diseases are endemic within populations and the analysis of such diseases are complicated by changing population demography. Motivated by the spread of cowpox among rodent populations, a combined mathematical model for population and disease dynamics is introduced. An MCMC algorithm is then constructed to make statistical inference for the model based on data being obtained from a capture–recapture experiment. The statistical analysis is used to identify the key elements in the spread of the cowpox virus.     

资本配置摩擦与中国经常项目波动

本文将国内资本市场摩擦和国际资本流动摩擦引入RBC模型,并采用贝叶斯方法校准模拟了中国经常项目的波动轨迹。研究结果表明：（1）国内资本市场摩擦和国际资本流动摩擦是形成中国经常项目波动的重要传导机制,两类资本市场摩擦机制的引入有助于准确拟合中国经常项目波动的波动性、协动性和持续性等各项特征;（2）贝叶斯估计得到的中国的资本调整成本和利率风险利差的参数值反映了中国资本配置效率和国际资本流动程度介于其他新兴市场经济体和发达经济体的水平之间;（3）中国经常项目波动主要由利率变动冲击和偏好冲击等两类结构性外生冲击通过国内资本市场摩擦机制和国际资本流动摩擦机制传导形成。     

Bayesian inference for stochastic multitype epidemics in structured populations via random graphs

Summary.  The paper is concerned with new methodology for statistical inference for final outcome infectious disease data using certain structured population stochastic epidemic models. A major obstacle to inference for such models is that the likelihood is both analytically and numerically intractable. The approach that is taken here is to impute missing information in the form of a random graph that describes the potential infectious contacts between individuals. This level of imputation overcomes various constraints of existing methodologies and yields more detailed information about the spread of disease. The methods are illustrated with both real and test data.