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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 (SAR err  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 SAR err  model, which led to a trend SAR err  model. Overall, BT spread from north-eastern to south-western France. The average trend SAR err -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 SAR err -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 SAR err  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.

Estimating front-wave velocity of infectious diseases: a simple, efficient method applied to bluetongue