Spatio-temporal epidemic modelling using additive-multiplicative intensity models

An extension of the stochastic susceptible-infectious-recovered (SIR) model is proposed in order to accommodate a regression context for modelling infectious disease surveillance data. The proposal is based on a multivariate counting process specified by conditional intensities, which contain an additive epidemic component and a multiplicative endemic component. This allows the analysis of endemic infectious diseases by quantifying risk factors for infection by external sources in addition to infective contacts. Simulation from the model is straightforward by Ogata's modified thinning algorithm. Inference can be performed by considering the full likelihood of the stochastic process with additional parameter restrictions to ensure non-negative conditional intensities. As an illustration we analyse data provided by the Federal Research Centre for Virus Diseases of Animals, Wusterhausen, Germany, on the incidence of the classical swine fever virus in Germany during 1993-2004

Poisson regression charts for the monitoring of surveillance time series

This paper presents a Poisson control chart for monitoring time series of counts typically arising in the surveillance of infectious diseases. The in-control mean is assumed to be time-varying and linear on the log-scale with intercept and seasonal components. If a shift in the intercept occurs the system goes out-of-control. Novel is that the magnitude of the shift does not have to be specified in advance: using the generalized likelihood ratio (GLR) statistic a monitoring scheme is formulated to detect on-line whether a shift in the intercept occurred. For this specific Poisson chart the necessary quantities of the GLR detector can be efficiently computed by recursive formulas. Extensions to more general Poisson charts e.g. containing an autoregressive epidemic component are discussed. Using Monte Carlo simulations run length properties of the proposed schemes are investigated. The practicability of the charts is demonstrated by applying them to the observed number of salmonella hadar cases in Germany 2001-2006

A space-time conditional intensity model for infectious disease occurence

A novel point process model continuous in space-time is proposed for infectious disease data. Modelling is based on the conditional intensity function (CIF) and extends an additive-multiplicative CIF model previously proposed for discrete space epidemic modelling. Estimation is performed by means of full maximum likelihood and a simulation algorithm is presented. The particular application of interest is the stochastic modelling of the transmission dynamics of the two most common meningococcal antigenic sequence types observed in Germany 2002–2008. Altogether, the proposed methodology represents a comprehensive and universal regression framework for the modelling, simulation and inference of self-exciting spatio-temporal point processes based on the CIF. Application is promoted by an implementation in the R package RLadyBug

Bayesian Estimation of the Size of a Population

We consider the following problem: estimate the size of a population marked with serial numbers after only a sample of the serial numbers has been observed. Its simplicity in formulation and the inviting possibilities of application make this estimation well suited for an undergraduate level probability course. Our contribution consists in a Bayesian treatment of the problem. For an improper uniform prior distribution, we show that the posterior mean and variance have nice closed form expressions and we demonstrate how to compute highest posterior density intervals. Maple and R code is provided on the authors’ web-page to allow students to verify the theoretical results and experiment with data

The R-Package 'surveillance'

This document gives an introduction to the R-Package 'surveillance' containing tools for outbreak detection in routinely collected surveillance data. The package contains an implementation of the procedures described by Stroup et al. (1989), Farrington et al. (1996) and the system used at the Robert Koch Institute, Germany. For evaluation purposes, the package contains example data sets and functionality to generate surveillance data by simulation. To compare the algorithms, benchmark numbers like sensitivity, specificity, and detection delay can be computed for a set of time series. Being an open-source package it should be easy to integrate new algorithms; as an example of this process, a simple Bayesian surveillance algorithm is described, implemented and evaluated

Methods for evaluating Decision Problems with Limited Information

LImited Memory Influence Diagrams (LIMIDs) are general models of decision problems for representing limited memory policies (Lauritzen and Nilsson (2001)). The evaluation of LIMIDs can be done by Single Policy Updating that produces a local maximum strategy in which no single policy modification can increase the expected utility. This paper examines the quality of the obtained local maximum strategy and proposes three different methods for evaluating LIMIDs. The first algorithm, Temporal Policy Updating, resembles Single Policy Updating. The second algorithm, Greedy Search, successively updates the policy that gives the highest expected utility improvement. The final algorithm, Simulating Annealing, differs from the two preceeding by allowing the search to take some downhill steps to escape a local maximum. A careful comparison of the algorithms is provided both in terms of the quality of the obtained strategies, and in terms of implementation of the algorithms including some considerations of the computational complexity

Statistical approaches to the surveillance of infectious diseases for veterinary public health

This technical report covers the aspect of using statistical methodology for the monitoring of routinely collected surveillance data in veterinary public health. An account of the Farrington algorithm and Poisson cumulative sum schemes for the detection of aberrations is given with special attention devoted to the occurrence of seasonality and spatial aggregation of the time series. Modelling approaches for retrospective analysis of surveillance counts are described. To illustrate the applicability of the methodology in veterinary public health, data from the surveillance of rabies among fox in Hesse, Germany, are analysed