Assessing the Impact of a Movement Network on the Spatiotemporal Spread of Infectious Diseases

Linking information on a movement network with space-time data on disease incidence is one of the key challenges in infectious disease epidemiology. In this article, we propose and compare two statistical frameworks for this purpose, namely, parameter-driven (PD) and observation-driven (OD) models. Bayesian inference in PD models is done using integrated nested Laplace approximations, while OD models can be easily fitted with existing software using maximum likelihood. The predictive performance of both formulations is assessed using proper scoring rules. As a case study, the impact of cattle trade on the spatiotemporal spread of Coxiellosis in Swiss cows, 2004-2009, is finally investigated.

[1]  P. Guttorp.  Stochastic modeling of scientific data , 1995 .

[2]  Haavard Rue,et al.  Estimation and extrapolation of time trends in registry data—Borrowing strength from related populations , 2011, 1108.0606.

[3]  I. Kiss,et al.  Modelling the initial spread of foot-and-mouth disease through animal movements , 2006, Proceedings of the Royal Society B: Biological Sciences.

[4]  Andrew Harvey,et al.  Forecasting, Structural Time Series Models and the Kalman Filter , 1990 .

[5]  S. Frühwirth-Schnatter,et al.  Auxiliary mixture sampling for parameter-driven models of time series of counts with applications to state space modelling , 2006 .

[6]  Leonhard Held,et al.  Gaussian Markov Random Fields: Theory and Applications , 2005 .

[7]  T. Geisel,et al.  Forecast and control of epidemics in a globalized world. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[8]  Leonhard Held,et al.  Using integrated nested Laplace approximations for the evaluation of veterinary surveillance data from Switzerland: a case‐study , 2011 .

[9]  A. Raftery,et al.  Strictly Proper Scoring Rules, Prediction, and Estimation , 2007 .

[10]  Matt J. Keeling,et al.  Networks and the Epidemiology of Infectious Disease , 2010, Interdisciplinary perspectives on infectious diseases.

[11]  S. Zeger,et al.  Markov regression models for time series: a quasi-likelihood approach. , 1988, Biometrics.

[12]  Claudia Czado,et al.  Predictive Model Assessment for Count Data , 2009, Biometrics.

[13]  S. Zeger.  A regression model for time series of counts , 1988 .

[14]  M. Hooten,et al.  A general science-based framework for dynamical spatio-temporal models , 2010 .

[15]  W. Li,et al.  Time series models based on generalized linear models: some further results. , 1994, Biometrics.

[16]  S. Chib,et al.  Posterior Simulation and Bayes Factors in Panel Count Data Models , 1998 .

[17]  Noel Cressie,et al.  Hierarchical statistical modelling of influenza epidemic dynamics in space and time , 2002, Statistics in medicine.

[18]  S. Merler,et al.  The role of population heterogeneity and human mobility in the spread of pandemic influenza , 2010, Proceedings of the Royal Society B: Biological Sciences.

[19]  D. Gamerman.  Markov chain Monte Carlo for dynamic generalised linear models , 1998 .

[20]  L. Held,et al.  Multivariate modelling of infectious disease surveillance data , 2008, Statistics in medicine.

[21]  Leonhard Held,et al.  A statistical framework for the analysis of multivariate infectious disease surveillance counts , 2005 .

[22]  F. Natale,et al.  Network analysis of Italian cattle trade patterns and evaluation of risks for potential disease spread. , 2009, Preventive Veterinary Medicine.

[23]  Elias Teixeira Krainski,et al.  Fitting dynamic models using integrated nested Laplace approximations - INLA , 2010 .

[24]  Sylvia Richardson,et al.  A hierarchical model for space–time surveillance data on meningococcal disease incidence , 2003 .

[25]  M. Nöremark,et al.  Network analysis of cattle and pig movements in Sweden: measures relevant for disease control and risk based surveillance. , 2011, Preventive veterinary medicine.

[26]  Michael Höhle,et al.  An R-package for the surveillance of infectious diseases , 2006 .

[27]  Christl A. Donnelly,et al.  The Foot-and-Mouth Epidemic in Great Britain: Pattern of Spread and Impact of Interventions , 2001, Science.

[28]  Leonhard Held,et al.  Improved auxiliary mixture sampling for hierarchical models of non-Gaussian data , 2009, Stat. Comput..

[29]  H. Rue,et al.  Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations , 2009 .

[30]  Michael Höhle,et al.  surveillance: An R package for the monitoring of infectious diseases , 2007, Comput. Stat..

[31]  E. Fèvre,et al.  Animal movements and the spread of infectious diseases , 2006, Trends in Microbiology.

[32]  L Held,et al.  Predictive assessment of a non‐linear random effects model for multivariate time series of infectious disease counts , 2011, Statistics in medicine.

[33]  Matthias Greiner,et al.  Relationship of trade patterns of the Danish swine industry animal movements network to potential disease spread. , 2007, Preventive veterinary medicine.

[34]  Helmut Ltkepohl,et al.  New Introduction to Multiple Time Series Analysis , 2007 .

[35]  J. Brownstein,et al.  Empirical Evidence for the Effect of Airline Travel on Inter-Regional Influenza Spread in the United States , 2006, PLoS medicine.

[36]  B. Leroux,et al.  Statistical models for autocorrelated count data , 2006, Statistics in medicine.

[37]  A. Pettitt,et al.  Bayesian analysis of a time series of counts with covariates: an application to the control of an infectious disease. , 2001, Biostatistics.

[38]  M. Gilbert,et al.  Cattle movements and bovine tuberculosis in Great Britain , 2005, Nature.