Logistic regression models integrating disease presence/absence data are widely used toidentify risk factors for a given disease. However, when data arise from imperfect surveil-lance systems, the interpretation of results is confusing since explanatory variables canbe related either to the occurrence of the disease or to the efficiency of the surveillancesystem. As an alternative, we present spatial and non-spatial zero-inflated Poisson (ZIP)regressions for modelling the number of highly pathogenic avian influenza (HPAI) H5N1outbreaks that were reported at subdistrict level in Thailand during the second epidemicwave (July 3rd 2004 to May 5th 2005). The spatial ZIP model fitted the data more effec-tively than its non-spatial version. This model clarified the role of the different variables:for example, results suggested that human population density was not associated withthe disease occurrence but was rather associated with the number of reported outbreaksgiven disease occurrence. In addition, these models allowed estimating that 902 (95% CI881-922) subdistricts suffered at least one HPAI H5N1 outbreak in Thailand although only779 were reported to veterinary authorities, leading to a general surveillance sensitivityof 86.4% (95% CI 84.5-88.4). Finally, the outputs of the spatial ZIP model revealed the spa-tial distribution of the probability that a subdistrict could have been a false negative. Themethodology presented here can easily be adapted to other animal health contexts.