Anthropogenic factors and the risk of highly pathogenic avian influenza H5N1: prospects from a spatial-based model

Paul, Mathilde; Tavornpanich, Saraya; Abrial, David; Gasqui, Patrick; Charras-Garrido, Myriam; Thanapongtharm, Weerapong; Xiao, Xiangming; Gilbert, Marius; Roger, Francois; Ducrot, Christian

Disease modelling and mapping was performed for the whole of Thailand at the subdistrict level. We ran two parallel models (one for chickens, one for ducks) since we assumed that the respective spatial patterns for chickens and ducks were different. We aimed to produce disease maps based on ''relative risk'', which was taken to be a ratio of the risk of HPAI in a given subdistrict to the average risk nationwide. The latter was estimated from the overall number of cases and the poultry farm population in Thailand. Due to the widely varying number of poultry farms in each subdistrict, and because of spatial dependency between the subdistricts [17] , we applied the hierarchical Bayesian approach described by Besag et al. [3] to the HPAI H5N1 data. This method made it possible to compute area-specific relative risk estimates [17] while considering spatial interactions through a spatial smoothing based on a Gaussian auto-regressive model [3] . We used a first order spatial interaction neighbourhood based on the contiguity between the spatial units. The original method in Besag et al. [3] uses a Poisson distribution to model the occurrence of cases, which is appropriate for rare, non-contagious diseases such as cancers in humans [15] or bovine spongiform encephalopathy in cattle [1] . However, due to the contagiousness of HPAI within each spatial unit, applying this method to HPAI would result in overdispersion compared to the Poisson distribution. We handled this problem by modelling the locally observed number of cases using a negative binomial distribution [14] , an approach that has been used to model influenza by Fraser et al. [7] . Monte Carlo Markov Chain (MCMC) simulations were used to estimate the parameters of the model, including the estimate of relative risk for each spatial unit [16] . The estimation was performed using LinBugs [21] , with 1 million iterations, each producing a random simulation of the relative risk for all of the statistical units (e.g. subdistricts). Geweke and Heidelberger-Welch tests were used to assess the convergence of the models [5] . Considering a long safety burn-in period, parameters were estimated from a subset of 3 000 of the random simulations (with a systematic step of 1 over 3 to overcome auto-correlation problems). From this subset of 3 000 simulations, we computed credible intervals containing 95% of the values of relative risk. We tested the link between the relative risk values in subdistricts on chickens and ducks using a Spearman rank order correlation test. The relative risk was mapped for chickens and ducks using ArcGIS software v.9.1 (ESRI Inc.). Maps made it possible to identify groups of subdistricts with either a significantly high or a significantly low risk of HPAIinfected flocks compared to the rest of the country.