Abstract
Understanding the spatial dynamics of an infectious disease is critical when attempting to predict where and how fast the disease will spread. We illustrate an approach using a trend-surface analysis (TSA) model combined with a spatial error simultaneous autoregressive model (SARerr model) to estimate the speed of diffusion of bluetongue (BT), an infectious disease of ruminants caused by bluetongue virus (BTV) and transmitted by Culicoides. In a first step to gain further insight into the spatial transmission characteristics of BTV serotype 8, we used 2007-2008 clinical case reports in France and TSA modelling to identify the major directions and speed of disease diffusion. We accounted for spatial autocorrelation by combining TSA with a SARerr model, which led to a trend SARerr model. Overall, BT spread from north-eastern to south-western France. The average trend SARerr-estimated velocity across the country was 5.6 km/day. However, velocities differed between areas and time periods, varying between 2.1 and 9.3 km/day. For more than 83% of the contaminated municipalities, the trend SARerr-estimated velocity was less than 7 km/day. Our study was a first step in describing the diffusion process for BT in France. To our knowledge, it is the first to show that BT spread in France was primarily local and consistent with the active flight of Culicoides and local movements of farm animals. Models such as the trend SARerr models are powerful tools to provide information on direction and speed of disease diffusion when the only data available are date and location of cases.
Highlights
Understanding the spatial dynamics of an infectious disease is critical when attempting to predict where and how fast the disease will spread
The trend SARerr model Based on backward selection from the full quadratic trend SARerr model we selected the model with the lowest Akaike’s Information Criterion (AIC) and minimum residual autocorrelation (minRSA) (Table 2)
All the trend SARerr models had lower AIC values and less spatial autocorrelation in the residuals than the simple trend-surface analysis (TSA) model, which did not account for spatial autocorrelation
Summary
Understanding the spatial dynamics of an infectious disease is critical when attempting to predict where and how fast the disease will spread. The use of simulation modelling for estimating the spread of infectious animal diseases has become common [1,2,3,4] Most of these modelling approaches are complex, based on spatially explicit, stochastic, state-transition or network models [2,5,6,7] or on diffusion equations [8,9]. While such modelling approaches require precise knowledge on the model parameters, available data on emerging animal diseases are often restricted to case reports providing only date and location. Disease progression was rapid: 2 000 infected farms across Belgium, Germany, The Netherlands, France, and Luxembourg in 2006 [12], more than 30 000 farms in 2007 with an expansion in range to Denmark, the United Kingdom, Switzerland, and the Czech Republic [12,15]
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